Blend the rice, almonds, and cinnamon in a high-speed blender. Blend until fully pulverized, stop and mix around if powder sticks to the bottom.
Add in 2 cups water, vanilla and sugar. Blend for about a minute. Transfer to a large container and add remaining water and milk. Mix well.
Cover and chill about 10 hours.
Strain the mixture through a fine mesh sieve into a pitcher and serve with ice.