Pour chai tea concentrate into a large container or pitcher. Stir in sugar. Add 8 inches stick cinnamon, torn basil, sliced lime, and sliced orange. Cover and chill 4 to 24 hours.
Strain mixture, discarding solids. Just before serving, slowly add club soda to chai mixture. Serve over ice cubes. If desired, garnish with additional cinnamon sticks, citrus slices, and whole basil leaves. Makes 10 (6-ounce) servings.