Combine 1 cup of the grapefruit juice with the sugar in a saucepan set over medium heat. Stir occasionally until the sugar is dissolved. Remove from heat.
In a bowl, combine the grapefruit and sugar syrup with the remaining grapefruit juice and Campari. Chill completely in the fridge.
Freeze the mixture in an ice cream machine according to manufacturer's instructions. After churning, let harden in the freezer for at least 2 hours before serving.
Calories: 157kcal, Carbohydrates: 37g, Protein: 1g, Fat: 1g, Sodium: 2mg, Potassium: 143mg, Fiber: 1g, Sugar: 35g, Vitamin C: 24mg, Calcium: 7mg, Iron: 1mg