The 22-year-old spent two years in the USA with New York Red Bulls and Orlando City before a short spell with Barnsley last season.
Rooney, who began his career with Macclesfield, impressed during the opening weeks of pre-season and was offered a 12-month deal by Kevin Blackwell.
The forward becomes the Shakers' second signing of the day after Chris Sedgwick also penned a 12-month contract.
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- New York Red Bulls