Bring 4 cups of water to a simmer. Right before it comes to a boil, turn the heat off and add rice, cinnamon stick, and vanilla. Let it soak for at least 2 hours.
After the rice has soaked and can break easily with your fingers, blend it in a high speed blender along with cinnamon stick.
Using a cheese cloth or fine strainer, strain rice mixture. Do not skip this step of your Horchata will be grainy.
Once strained, add rice mixture back to blender. Add oat milk, maple syrup, and ice to blender. You may need to make this in two batches.
Once it is blended, store in a large pitcher. Add more ice when it's ready to be served.