Born in Zalaegerszeg,[2] Csóka began his career at hometown club Zalaegerszegi TE, before joining English club Wolverhampton Wanderers in January 2017.
[3] Whilst a Wolves player he spent loan spells at Slovakian clubs DAC 1904 Dunajská Streda and ŠTK 1914 Šamorín.
[4] After being released by Wolves, in September 2020 he signed for AFC Wimbledon following a trial.
[5] He scored his first and only goal for Wimbledon in a 5-2 defeat at Charlton Athletic on 12 December 2020.
[6] On 4 July 2022, Csóka returned to Hungary to rejoin Zalaegerszegi for an undisclosed fee in order to be closer to his family.