HNL and FC Honka in Finland's Veikkausliiga, Vargić made his debut with NK Osijek in 1.
On 1 February 2016, both Croatian and Italian press reported that Lazio have signed Vargić for a fee of €2.7 million.
[9] On 3 September 2018, Vargić joined Cypriot club Anorthosis Famagusta on a season-long loan.
After spending two seasons in 3rd-tier Croatian club Krk, he retired from professional football in June 2024.
On 12 November 2014, he made his senior national team debut in a friendly game against Argentina, entering as a substitute for Lovre Kalinić.