The 22-year-old can play at the back or in midfield and is a long throw specialist.
Muggleton is from Melton Mowbray, Leicestershire and has also had spells playing at Gillingham, Barnet and Eastleigh prior to his move to Bootham Crescent.
The utility man is the son of former Leicester City and Stoke City goalkeeper Carl Muggleton and goes straight into the Boro squad for the Evo-Stik North game away at Mossley tomorrow.