Heat the oven to 400°F and line a baking sheet with foil for easy cleanup.
In a mixing bowl, stir together the soy sauce, olive oil, garlic powder, paprika, salt, and black pepper.
Add the chicken drumsticks to the bowl and turn them until each piece is coated with the mixture.
Place the drumsticks on the baking sheet with space between them and bake for 20 minutes.
Remove the pan from the oven and brush each drumstick generously with BBQ sauce.
Return the pan to the oven and bake for another 15 to 20 minutes until the sauce looks sticky and the chicken reaches 165°F inside.