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

Rithm Acquisition Corp.

(Exact Name of Registrant as Specified in Its Charter)

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

If this form relates to the registration of a class of securities pursuant to Section 12(b) of the Exchange Act and is effective pursuant to General Instruction A.(c) or (e), check the following box. x

If this form relates to the registration of a class of securities pursuant to Section 12(g) of the Exchange Act and is effective pursuant to General Instruction A.(d) or (e), check the following box. ¨

If this form relates to the registration of a class of securities concurrently with a Regulation A offering, check the following box. ¨

Securities Act registration statement or Regulation A offering Statement file number to which this form relates: 333-284207

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

N/A

(Title of Class)

Item 1. Description of Registrant’s Securities to be Registered.

The securities to be registered hereby are units, Class A ordinary shares, par value $0.0001 per share, and redeemable warrants to purchase Class A ordinary shares of Rithm Acquisition Corp. (the “Registrant”). The description of the units, Class A ordinary shares and warrants set forth under the heading “Description of Securities” in the Registrant’s prospectus forming part of its Registration Statement on Form S-1 (File No. 333-284671), originally filed with the Securities and Exchange Commission on February 3, 2025, as thereafter amended and supplemented from time to time (the “Registration Statement”), to which this Form 8-A relates is incorporated by reference herein. Any form of prospectus or prospectus supplement to the Registration Statement that includes such descriptions and that is subsequently filed is hereby also incorporated by reference herein.

Item 2. Exhibits.

Pursuant to the Instructions as to Exhibits for Form 8-A, no exhibits are required to be filed, because no other securities of the Registrant are registered on the New York Stock Exchange, and the securities registered hereby are not being registered pursuant to Section 12(g) of the Securities Exchange Act of 1934, as amended.

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.