A proposed return to former club Charlton Athletic had been on the cards for the 23-year-old earlier in the summer, but that deal collapsed before it could be completed, opening the door to a move abroad instead.
Rak-Sakyi will now try to find greater consistency in Turkish football, with Palace continuing to monitor his progress as they weigh up his long-term future at Selhurst Park.
Confirming the move on its official channels, Crystal Palace said: "We can confirm that Jesurun Rak-Sakyi has joined Kasımpaşa on loan until the end of the season."
The London club added: "Everyone at Crystal Palace wishes Jes the very best during his loan spell abroad."
It is Rak-Sakyi's second spell in Turkish football, having previously spent the first half of last season on loan at Çaykur Rizespor, where he scored four goals in 13 appearances.
In between his stints in Turkey, he also had a brief loan spell at Stoke City earlier this year, adding to a well-travelled résumé that already includes spells at Charlton, where he was the Championship's joint-top scorer at Premier League 2 level before his first loan there, and Sheffield United, where he scored seven times in 35 Championship appearances.
Born in Southwark, Rak-Sakyi came through the youth ranks at Chelsea before joining Crystal Palace's academy in 2019, and has represented England at both Under-20 and Under-21 level, but switched allegiance to earn a first senior cap for Ghana earlier this year. He will remain at Kasımpaşa for the whole of the 2026/27 campaign before returning to Crystal Palace next summer.
Rak-Sakyi has made just 10 senior appearances for Palace since making his debut back in 2021, with his development largely taking place away from Selhurst Park across a string of loan spells that have now taken in five different clubs.
Palace handed him a new five-year contract in 2022 as a show of faith in his long-term potential, even as he continued to be sent out to gain regular first-team experience elsewhere, and the club will be hoping his latest switch to Turkey can finally help him kick on and force his way into contention back in south London.