Remove turkey from brine and rinse. Pat dry with a towel, especially the cavity. Season liberally with dry rub and place into the refrigerator for four hours.
After four hours, preheat Smoker to 275 degrees using fruit wood.
Stuff cavity of the bird with oranges, lemons, onion, garlic, thyme, and rosemary. Then stuff butter between the skin and breasts, spreading it out with your hands all along the breast.
Tie up legs and wings with kitchen string, or tuck them to keep tight against the turkey.
Place turkey on the smoker, and insert your digital meat probe into the breast and thigh or leg. Smoke until the internal temperature of both reads 165 degrees (F). Use an instant read to check temp in various part of the turkey, even if the digital probes read 165 to confirm all parts of the turkey are cooked through.
Remove from smoker (will likely take 3 - 4 hours with a 12 - 14 pound bird) and cover with foil. Let cool for about 20 minutes. Then slice and serve.