<PAGE>   1
      As filed with the Securities and Exchange Commission on June 13, 1996


                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   -----------

                                    FORM 8-A

                FOR REGISTRATION OF CERTAIN CLASSES OF SECURITIES
                    PURSUANT TO SECTION 12 (b) OR (g) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                                GERON CORPORATION
             (Exact name of registrant as specified in its charter)

              DELAWARE                                      75-2287752
(State of incorporation or organization)                    (IRS Employer
                                                            Identification No.)

200 CONSTITUTION DRIVE, MENLO PARK, CA                        94025
(Address of principal executive offices)                    (Zip Code)

        Securities to be registered pursuant to Section 12(b) of the Act:

         Title of each class                 Name of each exchange on which
         to be so registered                 each class is to be registered

                Not Applicable                        Not Applicable

        Securities to be registered pursuant to Section 12(g) of the Act:

                         Common Stock, $0.001 par value
                                (Title of Class)

<PAGE>   2
Item 1.           Description of Registrant's Securities to be Registered

Incorporated by reference to the information set forth under the caption
"Description of Capital Stock" in the Company's Registration
Statement on Form S-1 (SEC File No. 333-05853) (the "Registration
Statement").

Item 2.           Exhibits

                           The following exhibits are filed as a part of this
Registration Statement:

                           1        Specimen certificate for Registrant's Common
                                    Stock.

                           2.1      Certificate of Incorporation -- incorporated
                                    herein by reference to Exhibit 3.1 of the
                                    Company's Registration Statement.

                           2.2      Form of Amended and Restated Certificate of
                                    Incorporation to be filed with the Delaware
                                    Secretary of State to effect the Company's
                                    1-for-3.4 reverse stock split --
                                    incorporated herein by reference to Exhibit
                                    3.3 to the Company's Registration Statement.

                           2.3      Bylaws - incorporated herein by reference to
                                    Exhibit 3.2 to the Company's Registration
                                    Statement.

                           2.4      Form of Amended and Restated Bylaws to be
                                    effective upon the closing of the Company's 
                                    initial public offering of shares of its
                                    Common Stock -- incorporated herein by
                                    reference to Exhibit 3.4 to the Company's
                                    Registration Statement.


                                      -2-

<PAGE>   3
                                    SIGNATURE

         Pursuant to the requirements of Section 12 of the Securities Exchange
Act of 1934, the Registrant has duly caused this Registration Statement to be
signed on its behalf by the undersigned, thereto duly authorized.

Date: June 12, 1996                         GERON CORPORATION


                                            By: /s/ David L. Greenwood
                                               ---------------------------------
                                            David L. Greenwood, Chief Financial
                                            Officer, Treasurer and Secretary

                                      -3-

<PAGE>   4
                                INDEX TO EXHIBITS


<TABLE>
<CAPTION>
                                                                                        Sequentially
   Exhibit No.                              Description                                 Numbered Page
   -----------                              -----------                                 -------------
<S>                 <C>                                                          <C>
       1            Specimen certificate for Registrant's Common Stock.

       2.1          Certificate of Incorporation -- incorporated herein by       Incorporated by reference
                    reference to Exhibit 3.1 of the Company's Registration
                    Statement
       2.2          Form of Amended and Restated Certificate of Incorporation    Incorporated by reference
                    to be filed with the Delaware Secretary of State to effect
                    the Company's 1-for-3.4 reverse stock split --
                    incorporated herein by reference to Exhibit 3.3 to the
                    Company's Registration Statement.
       2.3          Bylaws -- incorporated herein by reference to Exhibit 3.2    Incorporated by
                    to the Company's Registration Statement.                     reference
       2.4          Form of Amended and Restated Bylaws to be effective upon     Incorporated by reference
                    the closing of the Company's initial public offering
                    of shares of its Common Stock -- incorporated herein
                    by reference to Exhibit 3.4 to the Company's Registration
                    Statement.



</TABLE>


                                      -4-





<PAGE>   1

                                                                   EXHIBIT 1



<TABLE>
<S>                                                        <C>                                          <C>
           NUMBER                                                                                       SHARES

                                                            GERON

INCORPORATED UNDER THE LAWS OF                                                            SEE REVERSE FOR STATEMENTS RELATING
    THE STATE OF DELAWARE                                                                      TO RIGHTS, PREFERENCES,
                                                                                          PRIVILEGES AND RESTRICTIONS, IF ANY

                                                                                                   CUSIP 374163 10 3


This Certifies that










is the owner of



                      FULLY PAID AND NON-ASSESSABLE SHARES OF COMMON STOCK, PAR VALUE $0.001 PER SHARE, OF

                                                      GERON CORPORATION

      transferable only on the books of the Corporation by the holder hereof in person or by duly authorized Attorney
      upon surrender of this certificate properly endorsed. This certificate is not valid until countersigned and 
      registered by the Transfer Agent and Registrar.

         WITNESS the facsimile seal of the Corporation and the facsimile signatures of its duly authorized officers.


      Dated


                                                       GERON CORPORATION
                                                          CORPORATE
              /s/ David L. Greenwood                         SEAL                          /s/ Ronald W. Eastman
                                                           NOV. 28,
      VICE PRESIDENT AND CHIEF FINANCIAL OFFICER             1990                   PRESIDENT AND CHIEF EXECUTIVE OFFICER
                                                           DELAWARE



COUNTERSIGNED AND REGISTERED:
   U.S. STOCK TRANSFER CORPORATION
         (GLENDALE, CA)
           TRANSFER AGENT AND REGISTRAR

BY

                   AUTHORIZED SIGNATURE

</TABLE>




<PAGE>   2
        A statement of the powers, designations, preferences and relative,
participating, optional or other special rights of each class of stock or series
thereof
 and the qualifications, limitations or restrictions of such preferences
and/or rights as established, from time to time, by the Certificate of
Incorporation of the Corporation and by any certificate of determination, the
number of shares constituting each class and series, and the designations
thereof, may be obtained by the holder hereof upon request and without charge
at the principal office of the Corporation.

        The following abbreviations, when used in the inscription on the face
of this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:


<TABLE>
<S>                                                             <C>
TEN COM -- as tenants in common                                 UNIF GIFT MIN ACT -- _______________ Custodian _______________
TEN ENT -- as tenants by the entireties                                                  (Cust)                    (Minor)
JT TEN  -- as joint tenants with right of                                            under Uniform Gifts to Minors
           survivorship and not as tenants                                           Act _____________________________________
           in common                                                                                  (State)
                                                                UNIF TRF MIN ACT  -- ____________ Custodian (until age _______)
                                                                                        (Cust)
                                                                                     ________________  under Uniform Transfers
                                                                                         (Minor)
                                                                                     to Minors Act ___________________________
                                                                                                              (State)



                          Additional abbreviations may also be used though not in the above list.
</TABLE>



        FOR VALUE RECEIVED, _________________________________ hereby sell,
assign and transfer unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
   IDENTIFYING NUMBER OF ASSIGNEE
______________________________________

______________________________________



_______________________________________________________________________________
 (PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE)

_______________________________________________________________________________

_______________________________________________________________________________

________________________________________________________________________ Shares
of the capital stock represented by the within Certificate, and do hereby
irrevocably constitute and appoint

______________________________________________________________________ Attorney
to transfer the said stock on the books of the within named Corporation with
full power of substitution in the premises.

Dated ___________________________________



                                      X _______________________________________

                                      X _______________________________________
                                NOTICE: THE SIGNATURE(S) TO THIS ASSIGNMENT
                                        MUST CORRESPOND WITH THE NAME(S) AS
                                        WRITTEN UPON THE FACE OF THE CERTIFICATE
                                        IN EVERY PARTICULAR, WITHOUT ALTERATION
                                        OR ENLARGEMENT OR ANY CHANGE WHATEVER.


Signature(s) Guaranteed




By _____________________________________________
THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE
GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS
AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH 
MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION
PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15.