Stir together water and sugar in a saucepan. Bring to a boil, stirring until sugar dissolves. Remove from heat. Cool.
Stir in cranberry juice. Pour mixture into an 8" square pan. Cover and freeze 4 hours or until frozen. Remove from freezer; let stand 10 to 15 minutes. Shave ice by scraping with a fork. Scoop ice into glasses, and serve immediately, or store in an airtight container in freezer until ready to serve.