After debuting in the senior team at local club Gislaveds IF at age 16, Bojanić moved to Östers IF in Superettan, Sweden's second tier, in 2010. Around that time, he also attracted interest from several European clubs, reportedly Fulham and Heereenveen. In 2012, Bojanić made 12 appearances as Östers IF won Superettan and got promoted to the first division. In 2013, Bojanić made his debut in Allsvenskan, aged 18. Midway through the season, after making 14 appearances for Öster, he transferred to IFK Göteborg.
IFK Göteborg
Bojanić signed a four and a half-year contract with IFK Göteborg, but failed to make an impact at the club. He reportedly had disciplinary issues during his stay at IFK Göteborg and Bojanić later admitted that he once fell asleep during a team meeting. In total, Bojanić would only make 10 league appearances for the side.
On 15 July 2014, Bojanić moved to Helsingborgs IF. He reunited with his former coach from Öster, Roar Hansen, and soon established himself as a starting player at the club. Bojanić fell out of favour with manager Henrik Larsson in 2016 after the player had criticised his coach in the media. Helsingborg got relegated to Superettan the same year. In 2017, he went on loan to Östersunds FK in Allsvenskan, but failed to make an impact, only making 4 league appearances for the side. Bojanić played 29 games, scored 6 goals and provided 13 assists, as Helsingborg won a promotion to Allsvenskan in 2018. At the end of the season, he was voted as "Superettan Player of the Year".
Hammarby IF
On 26 November 2018, Bojanić moved on a free transfer to Hammarby IF, signing a three and a half-year contract. He played 29 games, scoring 4 goals and providing 11 assists, as Hammarby finished 3rd in the table. He vas voted as Allsvenskan "Player of the Month" in October, and "Hammarby Player of the Season" by the fans of the club at the end of the year. In January 2020, Bojanić signed a new three and a half-year contract with Hammarby.
International career
Between 2011 and 2014, Bojanić won several caps for both the Swedish U17 and U19 teams. Bojanić was called up to the Swedish senior squad for the training tour in early 2020. He made his debut in a 1–0 friendly win against Moldova on 9 January 2020. Three days later, on 12 January, he provided the assist to Simon Hedlund as Sweden won 1–0 against Kosovo. Manager Janne Andersson praised him as one of the best Swedish players during the tour.
Style of play
As a deep-lying playmaker, Bojanić is known for his strong passing game and technique. He is also a set piece-specialist.