Preheat the oven to 425ºF. Combine the smoked paprika, garlic powder, onion powder, cayenne pepper, oregano, salt, and pepper in a bowl.
Place the chicken drumsticks in a bowl and drizzle the cooking oil over top. Sprinkle the prepared seasoning over the drumsticks, then toss until they're evenly coated in oil and spices.
Place the seasoned drumsticks on a baking sheet with enough space around each so they're not touching. You can line the baking sheet with foil or parchment for easier cleanup, if desired.
Transfer the chicken to the oven and bake for 40 minutes, or until they reach an internal temperature of 175ºF, flipping the drumsticks once half-way through. Serve hot.