The 21-year-old, who had a loan spell with National League rivals Kidderminster last season and has not featured for the Hatters so far this season, was signed by Mariners boss Paul Hurst on Friday.
Robinson helped Luton win promotion back to the Football League in 2013-14, scoring two goals in 27 appearances.
The midfielder could make his debut for the Mariners in their home game against Torquay at Blundell Park on Saturday.
Midfielder Matt Robinson knows how to win