Stir garlic, olive oil, tomato sauce, and red wine vinegar in a large bowl. Season with basil, salt, and cayenne pepper. Add shrimp to the bowl and stir until evenly coated. Cover and refrigerate for 30 minutes to 1 hour, stirring once or twice.
Preheat grill for medium heat and lightly oil the grate.
Thread shrimp onto skewers, piercing once near tail and once near head. Discard marinade.
Cook shrimp on preheated grill until opaque, 2 to 3 minutes per side.
