Preheat barbecue to medium-high and lightly grease the grate. Stir ketchup with honey, orange zest, orange juice, Worcestershire sauce, rosemary, garlic, cumin and pepper. Divide in half. Toss one half with the drumsticks and marinate for 30 minutes. Reserve remaining sauce mixture.
Discard the marinade and grill the chicken, turning occasionally, for 15 minutes. Brush chicken all over with reserved sauce and grill for 5 minutes or until no longer pink near the bone.