POWER OF ATTORNEY

     Know all by these presents, that the undersigned hereby constitutes and
appoints Hazel M. Aker, the undersigned's true and lawful attorney-in-fact to:

  1.  execute for and on behalf of the undersigned, in the undersigned's
      capacity as an officer and/or director of Oncternal Therapeutics, Inc.
      (the "Company"), Forms 3, 4 and 5 in accordance with Section 16(a) of the
      Securities Exchange Act of 1934 and the rules thereunder;

  2.  do and perform any and all acts for and on behalf of the undersigned which
      may be necessary or desirable to complete and execute any such Form 3, 4
      and 5, and any amendments thereto, and timely file such form or report
      with the Securities and Exchange Commission and any stock exchange or
      similar authority; and

  3.  take any other action of any type whatsoever in connection with the
      foregoing which, in the opinion of such attorney-in-fact, may be of
      benefit to, in the best interest of, or legally required by, the
      undersigned, it being understood that the documents executed by such
      attorney-in-fact on behalf of the undersigned pursuant to this Power of
      Attorney shall be in such form and shall contain such terms and conditions
      as such attorney-in-fact may approve in such attorney-in-fact's
      discretion.

        The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any rights and powers herein
granted, as fully to all intents and purposes as the undersigned might or could
do if personally present, with full power of substitution or revocation, hereby
ratifying and confirming all that such attorney-in-fact, or such attorney-in-
fact's substitute or substitutes, shall lawfully do or cause to be done by
virtue of this power of attorney and the rights and powers herein granted. The
undersigned acknowledges that the foregoing attorney-in-fact, in serving in such
capacity at the request of the undersigned, is not assuming, nor is the company
assuming, any of the undersigned's responsibilities to comply with Section 16 of
the Securities Exchange Act of 1934.

        This Power of Attorney supersedes any Power of Attorney previously
granted by the undersigned with respect to the foregoing matters and shall
remain in full force and effect until the undersigned is no longer required to
file Forms 3, 4 and 5 with respect to the undersigned's holdings of and
transactions in securities issued by the Company, unless earlier revoked by the
undersigned in a signed writing delivered to the foregoing attorney-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 9th day of June, 2019.

                                  /s/ Richard G. Vincent
                                 ------------------------------
                                 Richard G. Vincent