In a large container, mix the cup of rice with a gallon of cold water. Let the rice soak overnight or for at least four hours.
Add the sugar, cinnamon stick, and sweetened condensed milk to the soaked rice and water. In batches, blend the mixed ingredients in a blender. Make sure that it blends long enough to pulverize the rice and cinnamon stick.
Pass the blended liquid through a fine mesh strainer. Discard the solids that are left behind.
Serve over ice, with a dusting of fresh ground cinnamon.