Terzi is a youth product of Altinova Belediyespor and Beşiktaş. On 18 March 2022, he signed his first professional contract with Beşiktaş. On 12 January 2023, he moved to Karacabey Belediyespor on loan in the TFF Second League where he began his senior career.[2] He made his professional debut with Beşiktaş in a 2–0 UEFA Europa Conference League win over Lugano on 14 December 2023, scoring his side's second goal.Terzi is a youth international for Türkiye, having played for the Türkiye U18s in 2021.