Combine water and rice in a bowl. Let soak, at least 30 minutes.
Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.
Stir milk, sugar, salt, and cinnamon stick into the saucepan. Simmer until thick and the consistency of pudding, about 20 minutes. Discard cinnamon stick before serving.
