The 38-year-old former Jamaica international played under Minstermen boss Russ Wilcox for the Iron.
Burton has represented 14 clubs across a professional career that started at Portsmouth in 1994.
He could make his debut for the League Two strugglers in Saturday's trip to Cheltenham and is eligible for the FA Cup tie against AFC Wimbledon.
York City have signed veteran Scunthorpe United striker Deon Burton on a one-month loan deal.