Robertson can play at Left Back or left midfield and is in the Scottish Under 21 squad for their game against Moldova next week.
The signing came unannounced which makes a change for the Millers with boss Mick Harford keeping a lid on all transfer talk, however he is happy to get his man and told the clubs official website, "Gregor is strong and athletic and he is just the kind of young and mobile player I am looking for. I am sure he will do a good job for us."