Born in Ćuprija, Stojković grown up in Ražanj, where he started playing football with the local football club Bukovik.[2] Later he moved to Red Star Belgrade youth academy, and signed his first professional contract with the club in June 2009, on a three-year deal.[3] He spent the next two seasons on loan at FK Sopot, playing regularly in the Serbian League Belgrade. In 2011, Stojković returned to his parent club and made his Serbian SuperLiga debut in a 4–0 home win over Smederevo in March 2012. He also recorded three appearances in the Serbian Cup, as they won the trophy. During the 2012–13 season, Stojković played on loan at Banat Zrenjanin and subsequently for Čukarički.
In July 2016, Stojković signed a three-year contract with German club 1860 Munich. The transfer was approximately €750,000, and the coach at the time was Kosta Runjaić.[4] The team at the time included one of Stojković's teammates from Montenegro's national selection, Stefan Mugoša.[4] In spite of coming to Munich injured, Stojković initially saw playing time, but fell out of rhythm after a coaching change.[5] After the club was relegated from the 2. Bundesliga, Stojković left as a free agent in 2017.[6]
Red Star Belgrade
On 12 June 2017, Stojković rejoined his home club Red Star Belgrade on a two-year deal.[7] On 18 December 2018, Stojković signed a contract extension with Red Star to the summer of 2022.[8]
Rapid Wien
On 30 August 2019, Stojković signed for Rapid Wien for an undisclosed fee believed to be in the region of €300,000. He signed a contract until 2022. However, he was sacked by the club officials after he reported an injury so he can go and watch the Serbian Cup final between his beloved Red Star and Partizan.
In May 2016, Stojković was called up to the Montenegro national team by coach Ljubiša Tumbaković.[9] Despite being called up in June 2019, Stojković (along with Mirko Ivanić and Serbian manager Tumbaković) refused to play for the national team against Kosovo. Tumbaković was sacked for his actions the next day.[10] Stojković has earned a total of 15 caps, scoring no goals.[11] His final international was a March 2019 European Championship qualification match against England.[12]