Run a piece of grapefruit around the rim of a rocks glass and dip the rim in a shallow dish of coarse salt. Fill with ice and set aside.
Combine grapefruit juice, lime juice, and simple syrup in a cocktail shaker filled with ice.
Shake well and pour into the prepared glass.
Top with club soda. Garnish with a lime wedge, if desired.
Stir and enjoy!