Preheat the oven to 375°F (190°C).
Rinse the chicken drumsticks under cold water, then drain and pat dry with paper towels.
Rub the dry rub generously onto the skin and meat of the drumsticks.
Transfer the chicken to a baking sheet lined with parchment paper and bake in the oven.
At the 20-minute mark, remove the chicken and brush it with olive oil.
Turn the chicken drumsticks to the other side and bake for an additional 10 minutes.
Check the doneness of the chicken by cutting a slit through the meat.
If the meat is not fully cooked, bake for an additional 5–10 minutes.
Serve the chicken with BBQ sauce.