Pour sugar, cinnamon, and rice into hot water; stir until sugar dissolves. Cover, and let stand at room temperature for at least 3 hours, but preferably overnight.
Stir in milk, then puree with a hand blender, or in batches in a standing blender until the rice resembles fine sand. Strain through several layers of cheesecloth, or through a very fine strainer. Serve over ice.
