Place the rice in a blender. Cover the blender with a lid and blend until the rice is in very small pieces.
Place the rice in a large bowl and cover with warm water. Add the cinnamon sticks. Cover and refrigerate for at least 8 hours.
Remove the cinnamon sticks and place the rice and water into the blender. Cover and blend until the mixture is as smooth as possible.
Line a strainer with a few layers of cheesecloth and place it over a large bowl. Pour the rice water through. Squeeze as much of the liquid out as you can. Discard the rice.
Stir the milk, vanilla extract and sugar into the rice water until the sugar is dissolved. Adjust sugar to your taste.