Career
Kojić joined Rad as a trainee in 2003. He made his debut for the senior team in the 2006-2007 season. In May 2008, Kojić broke his leg in a match against Sevojno, causing him to miss the entire 2008-2009 season.
On 3 February 2013, the day of his 23rd birthday, Kojić was transferred from Rad to Partizan, together with his teammate Predrag Luka.
Both players signed a three-and-a-half-year contract.