Combine sugar, water, and ginger in a small saucepan over medium-high heat. Bring to a simmer, and stir constantly until sugar is dissolved. Remove from heat and strain into a pitcher; discard solids. Let cool completely, 30 to 45 minutes.
Pour 1/4 cup cooled ginger syrup into a separate pitcher; reserve remaining ginger syrup for a later use. Stir in lime juice, sparkling cider, and vodka. Pour into 4 ice-filled glasses and garnish with lime wedges.