Allen, who was with the Cod'eads from down the A180 when Laws made an approach for him, spent the summer looking for a club eventually joining second division Peterbrough United on a one-year deal.
He is not figuring prominently in the first team outfit of the Posh, and joined the Pirates stating that he was looking for first team football.
"Bradley is a proven player with a good record. He's someone we've had in mind since the pre-season and we've kept chipping away so we're pleased to have got him," said Rovers assistant manager John Still.