Combine milk, uncooked rice, and stick cinnamon in a heavy medium saucepan; bring to a boil, then reduce heat. Cover the mixture and allow to simmer for 20 minutes, or until the rice is tender. Remove the stick cinnamon, if using.
Discard rum. Stir the raisins, sugar, and vanilla into the rice mixture.
Sprinkle ground cinnamon over mixture. Serve warm, or chilled.