Money started his senior career with St Mirren, whom he joined from Dailly Amateurs in 1978. As a result of his move to full-time football he was obliged to give up a career in the police force. He made his debut on 1 August 1978 when selected to face a Southampton side containing stars such as Peter Osgood and Ted McDougall, however the presence of established goalkeeper Billy Thomson limited his appearances at Love Street until 1984, when Thomson joined Dundee United.
Money became Saints regular goalkeeper after that point and became a fans favourite for his part in the side's 1987 Scottish Cup win. He played in over 400 matches for the Saints and holds a club record for playing in the most European games, eight in total. He is also their all-time top scoring goalkeeper with penalties in December 1992 against Cowdenbeath and Clydebank. Widely considered one of St Mirren's best ever goalkeepers, he earned selection to several Scotland national team squads without ever earning a cap.
In the later years of his career, Money became player-assistant manager to Jimmy Bone at St Mirren before leaving the Paisley club to become a manager in his own right at Stranraer. In his time with Stranraer he led the Blues to the Scottish Challenge Cup in 1997 and the Scottish Football League Second Division title in 1998. After leaving Stranraer in 1999 he joined his boyhood heroes, Ayr United, in a coaching capacity before replacing Gordon Dalziel as their manager in 2002. He left Somerset Park in 2004, briefly managing junior side Cumnock after that.
Money then joined Stenhousemuir as youth development director, where he gained a reputation of breeding young talents at the club. He replaced Des McKeown as manager in early November 2006. However, after a poor start to Season 2007-08, Money resigned, with a 7-0 thrashing from East Fife being the straw that broke the camels back.