Unroll crescent roll dough, and separate into 4 rectangles; pinch seams to seal.
Stir together sugar and cinnamon; sprinkle evenly over rectangles.
Roll up, jellyroll fashion, starting with a long side; press edges to seal. Cut each log into 5 slices, and place in a lightly greased 8-inch round cakepan.
Bake at 350° for 12 minutes.
Combine powdered sugar, milk, and vanilla, stirring until smooth; drizzle over warm cinnamon rolls.