Exhibit 24

                                POWER OF ATTORNEY

      Know all by these presents, that the undersigned hereby constitutes and
appoints Neena Reddy, Victor Lopez, Mark Nixdorf, Alan Kirshenbaum and Bryan
Cole signing singly and with full power of substitution, the undersigned's true
and lawful attorney-in-fact to:

      (1)   prepare, execute in the undersigned's name and on the undersigned's
            behalf, and submit to the U.S. Securities and Exchange Commission
            (the "SEC") a Form ID, including amendments thereto, and any other
            documents necessary or appropriate to obtain codes and passwords
            enabling the undersigned to make electronic filings with the SEC of
            reports required by Section 16(a) of the Securities Exchange Act of
            1934, as amended (the "Exchange Act"), or any rule or regulation of
            the SEC;

      (2)   execute for and on behalf of the undersigned, in the undersigned's
            capacity as an officer and/or director of Owl Rock Technology
            Finance Corp. II, Forms 3, 4, and 5 in accordance with Section
            16(a) of the Exchange Act and the rules thereunder, and any other
            forms or reports the undersigned may be required to file in
            connection with the undersigned's ownership, acquisition, or
            disposition of securities of the Company;

      (3)   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, or 5, any amendment or amendments
            thereto, or any other form or report, and timely file such form or
            report with the SEC and any stock exchange or similar authority;
            and

      (4)   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 of the 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 Exchange Act.

            This Power of Attorney 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 2nd day of November, 2021.

                                      /s/ Jonathan Lamm
                                      -------------------------------
                                      Jonathan Lamm