Soak rice, almonds and 1½ cups water in blender overnight. Blend until smooth. While blending, add cinnamon, sugar and vanilla. Line sieve with cheesecloth and put on top of a large pitcher. Pour contents of blender slowly through sieve. Gather ends of cheesecloth and squeeze out any excess. Thin out with the additional water, adding more or less to taste.
Serve immediately over ice.