Brine the turkey using the instructions noted above overnight in the refrigerator for at least 12 hours
Preheat the smoker to 225°F.
Remove the turkey from the brine, rinse it, and pat it dry. Rub the turkey with olive oil or melted butter. Mix paprika, garlic powder, onion powder, and black pepper, and season the turkey with the mixture.
Place the turkey in the smoker, breast side up, and close the lid. Smoke the turkey for 30-40 minutes per pound, or until the internal temperature reaches 170°F in the breast or thigh. Remember to check both sides of the turkey to ensure even cooking.
Let the turkey rest for 20-30 minutes before carving.