The young left-back will link up with Steve McNulty's side after deciding to leave the Yellows.
Sinnott featured heavily for the Pitching In NPL Premier Division side during pre-season but failed to make a senior appearance for the club once the regular season began.
Meanwhile, the Bucks have lost just one of their opening four matches and are currently 11th in the West Division.
Sinnott could make his debut against Grimsby Borough in the FA Trophy next weekend.
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