Add the rice and cinnamon stick to a blender. Pulse to slightly break up the rice, about 1 to 2 minute's worth. Add half the water, then blend another minute.
Transfer to a large bowl or pitcher and add the remaining water. Soak at room temperature for 3 to 4 hours.
Return the mix to the blender to process until smooth, work in batches as needed.
Strain through a cheesecloth or fine sieve, and pour into a pitcher. Stir in sugar, then chill for an hour or two, just to get it completely cold.
Stir before stirring, pour over ice, and garnish with ground cinnamon.