[2] Before his refereeing career, Robertson was a youth goalkeeper with Partick Thistle (where his brother Michael also had a short spell), Queen's Park and St.

Robertson replaced injured referee Willie Column just before kick off for the Scottish Cup semi final match between Celtic and Rangers.

In July 2023, Robertson refereed the Uefa Champions League Match between Hamrun Spar and Maccabi Haifa.

The same month Robertson also refereed the Europa Conference League match between Apoel Nicosia and Vojvodina.

In August and September 2023, Robertson refereed the Europa Conference League matches between Astana and Partizan, and Zrinjski Mostar and AZ Alkmaar.

The decision was criticised after the game with former referee Dermot Gallagher stating "I thought it was a foul and I was surprised this wasn’t referred [for a pitchside review]".

The match was called off twice by Robertson within hours of the scheduled kick off time due to a waterlogged pitch.

During the match VAR awarded Aberdeen a penalty for an apparent handball by Rangers defender John Souttar.

Robertson also failed to punish Celtic striker Kyogo for a challenge on Aberdeen goalkeeper Ross Doohan.

The Celtic player kicked Doohan in the head while chasing a through ball and the challenge has since been described as "reckless and shows a disregard for the opponent".