Okan Kocuk was born in 1995 in the Mustafakemalpaşa district of Bursa. Okan, who started playing football at Mustafakemalpaşaspor, transferred to Bursaspor’s youth academy in 2008. In 2015, he signed his first professional contract with Bursaspor. During the 2016-17 season, he was loaned to Bandırmaspor, a 1. Lig team, where he played a total of 25 matches—23 in the league and 2 in the Turkish Cup. In the 2017-18 season, he was loaned to another 1. Lig team, İstanbulspor, where he appeared in 37 matches—34 in the league and 3 in the Turkish Cup. Returning to Bursaspor for the 2018-19 season, he played 22 league matches and spent 1,980 minutes on the pitch. In the 2019-20 season, he signed a four-year contract with Süper Lig club Galatasaray. On July 9, 2021, it was announced that he was loaned to Giresunspor. In May 2022, after the season ended, he returned to Galatasaray.

On June 19, 2023, the player himself announced that he was leaving Galatasaray due to the expiration of his contract. He played a total of 29 matches for Galatasaray, keeping a clean sheet in 9 of them. In the 2023-24 season, Samsunspor, newly promoted to the Süper Lig, announced that they had signed him on a three-year contract.