Forrester, 25, was a youth player at Everton and has had spells in the Football League with Blackburn and Morecambe.
Chairman Paul Hilton said: “It’s a real coup for Radcliffe to bring a player of Anton’s quality to the club. It shows the ambition at the football club to progress and I truly believe this signing will help us reach the next level."
Forrester made his debut in the goalless draw with Runcorn Town in the FA Cup on Saturday, and also started against FC United in the BetVictor Northern Premier on Monday.
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