A journeyman, Barrowman played for 15 different sides during his career, including Inverness Caledonian Thistle, Ross County and Dunfermline Athletic in Scotland and Birmingham City and Walsall in England.
Loaned to Blackpool for the first three months of the 2004–05 season,[7] Barrowman made his debut against Sheffield Wednesday, coming on as a substitute in a 2–1 home loss.
[10] On 26 July 2006, Barrowman returned to Scotland and signed a one-year contract with Scottish Premier League club Kilmarnock,[11] but after initially failing to break into the first team he joined Queen of the South on a month's loan during September.
He hit terrific form during his first season with County, scoring a total of 29 goals, 24 in the league, which helped the club to win the Second Division championship.
Inverness Caledonian Thistle manager Craig Brewster captured his main transfer target on 25 June 2008 when, after much deliberation, Barrowman committed himself to a three-year contract with the club.
[20] On 12 October 2010, he returned to first-team duty after two months out with a broken foot to score a late equaliser against Partick Thistle in the semi-final of the Scottish Challenge Cup; Ross County won the penalty shootout to qualify for the final.
[25] On 26 March 2013, Dunfermline applied to enter into administration[26] Two days later the club announced that eight players had been made redundant with Barrowman amongst them.
[34] On 13 January 2015, the same day he left Morton, Barrowman signed for former club Dunfermline Athletic on a short term six-month deal.
[35] His season with Rovers was hampered by injury, though he did make 25 appearances across all competitions, scoring 4 times for the Scottish League One side.
[38] After retiring at the end of the 2015–16 season, Barrowman became Scottish brand manager for sportswear firm Joma at the beginning of 2017.