Combine sugar and 2 1/4 cups water in a saucepan; bring to a boil. Cook 5 minutes without stirring. Remove from heat; stir in juice.
Sprinkle gelatin over 2 tablespoons water in a small saucepan; let stand for 1 minute. Cook over low heat, stirring until gelatin dissolves. Remove from heat; cool slightly. Stir gelatin mixture and ginger into sugar syrup.
Pour mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon into a freezer-safe container; cover and freeze at least 8 hours.