In a large skillet over medium-low heat, brown the sausage until just cooked through. Transfer links to a plate lined with paper towels to drain fat.

Open the tube of cinnamon roll dough. Set the container of icing aside. Separate the rolls, then cut each roll in half.

Take a half roll and pinch the cut ends together to form a "mini roll" resembling the original whole roll. In your palms, flatten to an oblong disk. Lay a sausage on the disk. Wrap dough around the link; pinch dough closed to hold. Place seam side down on bake sheet sprayed with cooking spray. Repeat with remaining dough and links.