Robertson's first major film role came in 2004 when he starred alongside fellow Scottish actor James McAvoy in Inside I'm Dancing.
He then went on to play a small part in the 2005 film Kingdom of Heaven as an Angelic Priest. Following this, he had a big role in the 2005 French war film Joyeux Noel in which he played Jonathan, a young man whose brother was shot dead during WW1. Robertson then went on to play characters in numerous TV dramas, including Luther, where he played both of the Millberry twins, a murderous duo who decided their victim's fate on the roll of a die.
Robertson returned to his home in Shetland to film the TV series of the same name, where he starred as Constable Sandy Wilson in the BBC One adaptation of the popular Ann Cleeves book series. The show was criticised for its lack of Shetland accents, with Robertson being the only main cast member born and brought up on the islands. However, the series attracted over 6 million viewers and a second series was commissioned featuring, alongside Douglas Henshall and Robertson, actors Brian Cox, Julie Graham and Alex Norton, with Robertson's character now as a detective. Robertson stated to Digital Spy that his portrayal of Constable Wilson was a "nice break from playing killers and creeps". A third series, telling a single story, aired in 2016.
The fourth season of Shetland was broadcast in early 2018 on BBC One, with Robertson returning as Detective Wilson.
