Born in Priboj,[2] Šipčić started his career at the local club FAP. Playing as a senior, Šipčić appeared in the Drina Zone League as a bonus player until the end of 2013, when he left the club.[3] At the beginning of 2014, Šipčić joined Serbian SuperLiga side OFK Beograd and passed the winter break off-season with the first team.[4] After the end of 2013–14 Serbian SuperLiga season, when he overgrown youth selection, Šipčić left the club without official caps.[2]
Rad
In summer 2014, Šipčić joined Rad reserves, Žarkovo. He stayed with the club for two seasons, scoring three goals on 46 matches in the Serbian League Belgrade.[2] In summer 2016, Šipčić promoted in the first team and signed a three-year professional contract with Rad.[5] He made his SuperLiga for Rad in 18 fixture match of the 2016–17 Serbian SuperLiga season against Radnički Niš, replacing injured Stevan Bates.[6] Previously, he made an official debut for the club in a Serbian Cup match against Mladost Lučani, played on 26 October 2016.[7] Through the first season in professional football, Šipčić made 4 competitive matches at total.[8] During the 2017–18 Serbian SuperLiga campaign,[9] Šipčić was also a part of the first squad under coaches Gordan Petrić, Slađan Nikolić and Zoran Milinković, making 25 appearances in both domestic competitions.[8] In summer 2018, Šipčić extended his contract with Rad on a three-year deal until June 2021.[10] Šipčić noted his first goal for Rad in 3rd fixture match of the 2018–19 Serbian SuperLiga campaign, scoring in 2–1 away victory over Vojvodina on 5 August 2018.[11]
Tenerife
On 30 July 2019, Šipčić moved abroad and signed a three-year deal with Spanish Segunda División side CD Tenerife.[12] On 21 July 2023, he renewed his contract until 2027,[13]
On 7 July 2024, Šipčić was loaned to fellow second division side FC Cartagena, for one year.[14]
International career
Born in Priboj, Serbia, Šipčić is of Montenegrin descent.[15] He was called up to represent the Montenegro national team for a set of friendlies in March 2022. On 24 March 2022, he debuted with Montenegro in a 1–0 friendly loss to Armenia on 24 March 2022.[16]