Combine olive oil, ketchup, balsamic vinegar, garlic, cilantro, paprika, salt, and cayenne pepper in a large bowl. Add shrimp and coat well. Chill in the refrigerator for 30 minutes to 1 hour.
Preheat a grill for medium-high heat and lightly oil the grate. Thread shrimp onto skewers.
Cook shrimp on preheated grill until pink and opaque, 2 to 3 minutes on each side.