Pour the rice and water into a blender and blend at least 1 minute, or until the rice just begins to break up. Add the cinnamon sticks to the rice and water and let stand at room temperature for a minimum of 3 hours.
Strain the rice water through fine mesh or cheesecloth into a pitcher and discard the rice. Stir the milk, vanilla, cinnamon, and sugar into the rice water. Chill and stir before serving over ice.