McNulty, 36, has made more than 600 career appearances, and has previously featured for Fleetwood Town, Tranmere Rovers and Luton Town.
He began his career at Liverpool and skippered the Reds at under 19s level before his release from the Anfield club in 2003.
The Liverpool-born centre-back moved onto non-league football, starting at Burscough before moving to Vauxhall Motors and then Barrow, with whom he captained to promotion into the Conference.
The central defender joins Isaac Baldwin, Scott Bakkor, Josh Gregory, Steven Tames and James Hooper as new arrivals in to Carl Macauley's squad at Wincham Park.
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