The former West Ham United youngster made 39 appearances for The Hamlet in the 2014/15 season and earned a move into the professional game signing for Leyton Orient and then Accrington Stanley.
Recently Shaw has been with both East Thurrock United and Woking respectively.
The 22-year-old England C International returns on a short-term deal after a pre-season disrupted by injury along with the recent absence of Nathan Green.