Bring water to a boil with 1/4 teaspoon salt in a large heavy saucepan. Stir in rice and return to a boil. Cook, covered, over low heat until water is absorbed, about 18 minutes.
Stir in milk, sugar, zest, and cinnamon stick and simmer, uncovered, stirring often, until thickened and rice is tender, 40 minutes to 1 hour. Stir in vanilla. Cool to lukewarm in a large shallow bowl, surface covered with a piece of buttered wax paper.