The 20-year-old has arrived on an initial one-year contract, with the option of a second, after leaving Premier League side Nottingham Forest.
His football background includes five years on the books at Old Trafford with Manchester United.
Norkett enjoyed a loan spell in League Two with Cheltenham Town last season – and now arrives at the Jakemans Community Stadium looking to kick-start his senior career.
He scored his first EFL goal for the Robins against Accrington Stanley in October.