Robertson began his career with Dundee, but made his senior debut while on loan at Peterhead, spending the second part of the 2003–04 season at Balmoor.

In January 2005, shortly after returning to Dens Park, he made his Dundee debut, going on to feature in ten matches that season and attracting interest from Craig Levein at Leicester City.

Four days later, Robertson scored his first league goal, netting the third in a 3–0 win over Hearts and by mid-November, had played every minute of United's matches that season.

In January, however, an osteitis pubis diagnosis ruled him out for the remaining few months of the season,[9] although he made one substitute appearance in May.

In October the Dundee director, Calum Melville, publicly stated he was planning to bid £500,000 for the Scotland international in the January transfer window.

Craig Levein, the United manager, criticised the Dundee director by suggesting he needs tutored in the workings of football.

Robertson also made two appearances in the Europa League, but Dundee United were eliminated in the qualification round against Greek side AEK Athens.

Two months later, on 7 January 2012, in the fourth round of the Scottish Cup, Robertson scored and provided an assist for Gary Mackay-Steven in a 6–2 win over Airdrie United.

[24] After the match, Robertson said he might stay at Dundee United,[25] although many clubs in England including Birmingham City,[26] Brentford[27] and Blackpool.

[30] However, it didn't go to plan as his first team opportunities where he spent most of his time at the club on the bench or not in the squad and only made one appearance.

[33] He later admitted that he should have scored for Hibs earlier than that, particularly when he missed an easy chance in a Scottish Cup tie against Falkirk.

[35] Although he continued to be involved in the first team after Terry Butcher became manager,[36] Robertson sustained medial knee ligament damage in February 2014.

[57] The game ended in a 3–3 draw and Robertson missed the decisive kick in a penalty shootout, which meant that Raith were relegated to League One.

[58] After a change of ownership and management at United meant that he was allowed to play for another club while coaching with them, Robertson signed for Brechin City in January 2019.

[63] Robertson would remain assistant manager of Forfar until the end of the season, where he would leave the role to take a more 'enhanced' position with Dundee.

[64] Scott's mother Diane Robertson (née McLaren) was a footballer and Scottish internationalist who played for her country seventeen times during the 1970s.

[66] Robertson attended Dundee's Braeview Academy, alongside fellow future footballers Garry Kenneth and Charlie Adam.