The 25-year-old attracted interest from Football League clubs last season after netting 14 times for the Blue Square Premier outfit, but has dropped down the pecking order this term.
Rankine has joined the Cherries on an initial one-month loan deal.
"A number of league clubs had enquired about him, they've got a lot of good strikers at Rushden so it's good we've signed him," the Cherries manager Jimmy Quinn said.
"I felt we needed a bit of extra firepower up front and something different in attack."
Rankine made 24 appearances, mostly off the bench for Scunthorpe after joining from Barrow in September 2004.
But after only scoring once - a dramatic winner on his debut against Bury - he was released in January 2006.