The 21-year-old has recently returned to Highbury Stadium following a successful loan spell in National League North with Hereford FC.
With Cameron Gregory working his way back to full fitness and Aidan Stone having returned to Notts County at the conclusion of his loan spell, Donaghy's arrival is a welcome one for manager Graham Coughlan.
Donaghy will wear squad number 13 during his time at the Jakemans Community Stadium – and trained with his new team-mates for the first time on Tuesday.
Elsewhere on Tuesday, Gregory played 45 minutes as the Pilgrims' under-23s travelled to Huddersfield Town B in a behind-closed-doors friendly.
Luca Alonzi was on target for United in a 3-1 defeat – with full-back Kieran Coates also completing 90 minutes.