On 2 March 2013, Škrbić scored on his official debut for OFK Beograd after coming on as a substitute in a 3–1 home loss to Jagodina.[2] In September 2016, Škrbić joined Slovenian club Krško.[3] He left Krško in 2018 and joined Giresunspor in January 2019.[4] On 6 February 2020, Škrbić signed a two-and-a-half-year contract with Bosnian Premier League club Zrinjski Mostar.[5] He made his official debut for Zrinjski in a 2–0 league win against Čelik Zenica on 23 February 2020.[6] Škrbić terminated his contract with Zrinjski and left the club in June 2021.[7]