Preheat your smoker to 275°F (135°C). If you don't have a dedicated turkey fryer, create an indirect heating method using foil-lined disposable pans and aluminum balls.
Mix together the salt, pepper, garlic powder, and brown sugar in a small bowl to make your dry rub. Pat down any excess moisture from both sides of the turkey with paper towels. Tie legs together tightly using kitchen twine.
Rub half of the seasoning mix generously all over the outside and inside cavity, making sure it's well coated. Tuck wings behind back if possible for better smoking results. Place turkey breast side up on a rack in your prepped pan(s), with some space between each bird to allow smoke penetration.
Smoke the turkey until an internal thermometer reads 165°F (74°C) when inserted into the thickest part of thigh, without touching bone. This usually takes around 3-4 hours depending on your smoker and size of bird. Once cooked through, let turkey rest for at least half an hour before carving to allow juices redistribute.
Carve into slices or drumsticks as desired.