Scott started his career at Heart of Midlothian where he spent seven years while also representing Scotland at international youth level. He made his first team debut for the club as a substitute against Inverness in April 2008 making him the youngest player ever to have played competitive football for Hearts in the Scottish Premiership. He was 16 years, 1 month and 14 days old.
In the summer of 2015, Robinson joined Kilmarnock on a three-year-deal but after only one season in East Ayrshire was released from the club. A move to Dunfermline Athletic was next in line, and after a successful trial, Scott signed on a short-term contract through until the end of the 2015/2016 season.
A further spell at Scottish League One club East Fife followed before Livingston announced a pre contract agreement had been reached with Robinson in May 2017.
After four years at Livingston, Scott was released from the club having been a pivotal part in helping them to a top sixth finish in the league as well as reaching the Betfred Cup Final in his final season.
Robinson moved on and signed a two-year contract at Kilmarnock in June 2021.