Born in Loznica, Kojić joined Rad as a trainee in 2003. He made his senior debuts in the 2006–07 season, recording three appearances in the process. In May 2008, Kojić broke his leg in a match against Sevojno, causing him to miss the entire 2008–09 season. On 2 May 2010, he scored his first senior career goal, finding the back of the net in a 1–0 home win over Jagodina.[2] On 30 June 2011, he scored a goal and provided three assists in a 6–0 home win over Tre Penne in the first leg of Europa League first qualifying round.[3] One week later, he scored twice in the return leg against Tre Penne in a 1–3 away win.[4] On 19 August 2012, Kojić scored twice in a 2–2 away draw against Red Star Belgrade.[5] He scored another brace on 1 September 2012 in a 2–3 away league win over Spartak Subotica.[6]
Partizan
On 3 February 2013, on his 23rd birthday, Kojić was transferred to Partizan, together with Predrag Luka. Both players signed a three-and-a-half-year contract.[7] Kojić made his debut for Partizan against Donji Srem on 2 March 2013.[8] Four days later, Kojić scored his first two goals for Partizan in a 4–0 away league win over BSK Borča.[9]
On 26 April 2014, Kojić scored the winning goal in the 90th minute of the Belgrade derby in a 2–1 home win over Red Star Belgrade.[10] On 3 May 2014, Kojić scored a hat-trick in a 5–0 away win over Donji Srem.[11] He finished the season as the club's top scorer with eight goals.
Gaziantep BB
In August 2016, Kojić joined Turkish second-tier side Gaziantep BB, signing a three-year contract and was given the number 36 shirt.[12]
Radnički Niš
On 15 February 2017, Kojić returned to his homeland and signed with Radnički Niš until the end of the 2016–17 season.[13]
Tokyo Verdy
On 16 January 2019, Tokyo Verdy announced the signing of Kojić.[14]