"I'm delighted Hakan is joining us," said Rovers boss Graeme Souness.
"I know what he's capable of, having worked with him before.
"He's a natural athlete and will provide us with something different.
"He is carrying a slight injury at the moment but that has been taken into account and we are confident he will strengthen our squad."
Sukur, who has won 80 caps for Turkey, has been without a club since being released by Parma in the summer.