How to Make It
Stir together kosher salt, light brown sugar, paprika, dried oregano, cayenne pepper, and garlic powder in a small bowl; set Cajun rub aside.
Remove giblets and neck from turkey; reserve for another use. Pat turkey dry with paper towels. Rub 1 tablespoon Cajun rub in cavity. Reserve 1 tablespoon Cajun rub, and sprinkle outside of turkey with remaining Cajun rub; rub into skin. Chill turkey, uncovered, 10 to 24 hours.
Stir together butter and reserved 1 tablespoon Cajun rub. Loosen skin from turkey breast without totally detaching skin; spread butter mixture under skin. Replace skin, securing with wooden picks. Tie ends of legs together with kitchen twine, tuck wing tips under, and let stand at room temperature 30 minutes.
Meanwhile, prepare charcoal fire in smoker according to manufacturer’s instructions, bringing internal temperature to 225°F to 235°F. Maintain temperature inside smoker 15 to 20 minutes. Place hickory chips on coals. Smoke turkey, breast side up, covered with smoker lid, until a thermometer inserted in thickest portion of turkey registers 155°F, 5 to 6 hours.
Remove turkey from smoker, cover loosely with heavy-duty aluminum foil, and let stand 20 minutes before slicing.