Career
Born in Podgorica, he played in the youth team of OFK Beograd before making his debut as senior playing on loan with OFK Mladenovac and with Montenegrin First League side. With the OFK Beograd first-team he made 3 appearances in the first half of the 2012-2013 Serbian SuperLiga. During the winter break of the 2013-2014 season he left OFK Beograd and joined permanently.
On 13 February 2014, Dragojević signed a one and a half year contract with Velež Mostar playing in the Bosnian Premier League.
On 30 August 2015, Dragojević moved clubs again but this time to Albanian Superliga club Vllaznia Shkodër. On the national team level, Dragojević represented Montenegro at U-19 level