Born in İzmir, Özkacar spent his youth career at local teams Bucaspor, Altinordu and Altay.[2] He made his professional debut in 2018, while on loan at Karacabey Belediyespor, before returning to Altay the following year.[2]
Lyon
On 18 August 2020, Özkacar joined Ligue 1 club Lyon on a five-year deal.[3] On 21 April 2021, he made his debut for Lyon as a late substitute for Léo Dubois during a 2–0 loss to Monaco in the Coupe de France.[4]
In August 2022, Özkacar signed on loan for La Liga side Valencia.[6] On 1 July 2023, the club exercised their buy-option in the loan contract, signing him permanently on a five-year contract.[7]
However, Özkacar scored an own-goal in a 1-0 loss against Deportivo Alavés,[8] and only started 35% of matches in La Liga by January 2024, leading some media outlets to report he was seeking a move away in order to make it in Turkey's UEFA Euro 2024 squad.[9]
Loan to Valladolid
On 29 August 2024, Özkacar was loaned to fellow Spanish top tier side Real Valladolid on a one-year deal.[10]