Combine all ingredients in a Dutch oven; bring to a boil. Reduce heat, and cook 15 minutes or until all cranberries pop. Strain cranberry mixture through a fine sieve over a bowl, discarding solids. Cover and chill.
Pour the cranberry mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon cranberry ice into a freezer-safe container; cover and freeze 1 hour or until ready to serve.