
The 21-year-old, who spent his formative years in the academy at Manchester City, made 43 appearances during a loan spell in the EFL with Grimsby Town last season, scoring four goals in the process.
Barrington has been without a club so far this season – but now joins Paul Hurst's evolving squad for the closing weeks of the National League campaign.
He is registered and eligible to make his debut against Woking on Tuesday evening, having been allocated squad number 7.