Combine olive oil, lime juice, garlic powder, onion powder, chili powder, oregano, parsley, and pepper in a gallon-size resealable plastic bag. Add chicken drumsticks, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator at least 2 hours and preferably overnight.

Preheat the oven to 425 degrees F (220 degrees C).

Meanwhile, line a baking sheet with aluminum foil. Remove drumsticks from marinade, shake off excess, and arrange on the baking sheet. Discard remaining marinade. Let chicken come to room temperature until the oven has preheated.

Roast in the preheated oven until browned, about 25 minutes. Flip chicken and baste with juices; continue cooking until browned on the second side, 10 to 15 minutes more. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).

Cover chicken with aluminum foil. Let stand before serving, about 5 minutes.