[6] Murdoch become a first team regular in the 2014–15 season as Rangers aimed to gain promotion from the Scottish Championship, They finished a disappointing third behind Hearts and Hibernian but qualified for the Premiership Play Offs.
Rangers beat Queen of the South and Hibernian to reach the final where they faced 11th placed Scottish Premiership club Motherwell.
Murdoch played all the play-off games and for his performances over the season won the Rangers' Young Player of the Year award in May 2015.
On 1 September 2015, he moved to Scottish League One side Cowdenbeath on a six-month loan deal until January 2016.
Murdoch scored the only goal in a 1–0 win for Queens against Hibernian, which helped to extend Rangers' lead in the 2015–16 Scottish Championship.
On 12 July 2018, Murdoch signed a one-year deal with Scottish Championship side Ayr United.