Combine water and cranberries in a large saucepan. Bring to a boil over high heat; boil 8 to 10 minutes or until skins pop. Remove from heat. Process cranberries, in batches, in a food processor until coarsely pureed. Press pureed cranberries through a wire-mesh strainer into a bowl, discarding solids. Add sugar and remaining 4 ingredients to cranberry puree, stirring until sugar dissolves.
Cover and freeze until firm.
To serve, remove from freezer and thaw. Mix with ginger ale or seltzer.