To make the ginger syrup, combine sugar, water, and ginger in a small saucepan over low heat. Simmer for 10 minutes, then strain out ginger pieces and allow to cool to room temperature.
In a cocktail shaker with ice, combine 1/2 oz ginger syrup, grapefruit juice, lemon juice, and gin. Shake well.
Pour soda water into a collin’s glass over ice. Pour in cocktail ingredients, stirring gently. Garnish with rosemary.