After beginning his senior career with Montrose, Murray played for several junior clubs before returning to senior football with Arbroath in 2014. He signed for Dundee United in January 2015, but initially remained with Arbroath on loan. His father Gary Murray was also a professional football player, playing for Montrose and Hibernian.
After playing for a number of youth teams, including Dundee Celtic Boys Club, Dee Club and Dundee United Social Club, Murray joined Montrose as a youth player.
Murray began his professional career with Montrose. He made his only appearance for the first team as a substitute against Queen"s Park at Hampden in May 2011.
After a spell on loan to Dundee-based junior club Downfield, Murray was released by Montrose and joined another junior club, Tayport, in February 2012. After leaving Tayport, Murray spent almost a year living in Australia.
On his return to Scotland, he briefly played junior football for Dundee Violet before signing for Arbroath in May 2014.
After scoring 18 goals in 28 matches, Murray was signed by Dundee United for a £50,000 fee in January 2015, but immediately loaned back to Arbroath for the rest of the 2014-2015 season. Murray made his debut for Dundee United against Aberdeen in August 2015.