[1] Rašić started his career, alongside his identical twin brother Damir, in their hometown club Zmaj Makarska, before moving on to the Hajduk Split academy.
Despite alleged interest from Panathinaikos,[2] and games for the Croatia U19 team,[3] the brothers didn't get contracts with Hajduk Split, and signed with the Druga HNL team Mosor.
Not getting a chance at Split, he moved on to Varaždin, playing there until the club was suspended.
In the summer of 2012 Rašić rejoined his first club Zmaj Makarska in the Treća HNL Jug for a season, followed by another half-season stint at Imotski at the same level.
At the beginning of 2014, Rašić joined the Slovenian PrvaLiga team Krka.