| Cover | Feb. 26, 2025 |
| Document Information [Line Items] | |
| Document Type | 8-K |
| Amendment Flag | false |
| Document Period End Date | Feb. 26, 2025 |
| Current Fiscal Year End Date | --09-30 |
| Entity File Number | 001-42537 |
| Entity Registrant Name | Rithm Acquisition Corp. |
| Entity Central Index Key | 0002047497 |
| Entity Tax Identification Number | 98-1832772 |
| Entity Incorporation, State or Country Code | E9 |
| Entity Address, Address Line One | 799 Broadway |
| Entity Address, Address Line Two | 8th Floor |
| Entity Address, City or Town | New York |
| Entity Address, State or Province | NY |
| Entity Address, Postal Zip Code | 10003 |
| City Area Code | 212 |
| Local Phone Number | 850-7770 |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Entity Emerging Growth Company | true |
| Elected Not To Use the Extended Transition Period | false |
| Units Each Consisting Of One Classa Ordinary Share 0. 0001 Par Value And Onethird Of One Redeemable Warrant [Member] | |
| Document Information [Line Items] | |
| Title of 12(b) Security | Units, each consisting of one Class A ordinary share, $0.0001 par value, and one-third of one redeemable warrant |
| Trading Symbol | RAC.U |
| Security Exchange Name | NYSE |
| Classa Ordinary Shares Included As Part Of Units [Member] | |
| Document Information [Line Items] | |
| Title of 12(b) Security | Class A ordinary shares included as part of the units |
| Trading Symbol | RAC |
| Security Exchange Name | NYSE |
| Redeemable Warrants Included As Part Of Units Each Whole Warrant Exercisable For One Classa Ordinary Share At Exercise Price Of 11. 50 [Member] | |
| Document Information [Line Items] | |
| Title of 12(b) Security | Redeemable warrants included as part of the units, each whole warrant exercisable for one Class A ordinary share at an exercise price of $11.50 |
| Trading Symbol | RAC.WS |
| Security Exchange Name | NYSE |
