In large container, mix 6 cups warm water with rice, almonds and cinnamon stick. Cover and soak at least 12 hours, or up to 24 hours.
Blend rice-water mixture with sugar in batches until rice is thoroughly ground (liquid will feel only slightly gritty between fingers), about 3 minutes per batch.
Strain rice mixture into large pitcher through very fine mesh strainer lined with 2 layers of damp cheesecloth, pouring slowly and pressing on solids with spatula to extract as much liquid as possible. Discard any leftover rice-almond pulp. Stir 6 cups cold water into pitcher.
To serve, thoroughly stir horchata. Pour into glass with ice.