Make the brine. Add ½ gallon water to a large stockpot and bring to a boil. Add kosher salt, sorghum, lemons, oranges, and Cajun seasoning. Stir until the salt and sorghum dissolve. Remove from heat and let cool slightly.
Set up the brining bucket. Add about 7 pounds of ice to a clean 5-gallon bucket. Pour in the cooled brine.
Prep the turkey for brining. Remove the neck and giblets from the cavity. Submerge the thawed turkey completely in the brine. Top with the remaining ice and weigh it down with a plate if it floats. Keep the brine under 40°F. Brine 12 to 24 hours, about 1 hour per pound.
Optional crispy skin step. Remove the turkey from the brine. Rinse under cool water and pat completely dry. Place on a wire rack set over a sheet pan and refrigerate uncovered for at least 8 hours to form a pellicle that promotes browning and crisp skin.
Truss and season. Tie legs and wings snug to the body with twine. If desired, apply a very light dusting of BBQ rub.
Preheat the smoker. Heat to 325°F. Choose light to medium smoke. Apple, cherry, or peach work well. Oak is fine if used lightly. Avoid mesquite for poultry.
Prep the skin. Right before the turkey goes on the smoker, pat away any condensation. Brush a light coat of melted butter or canola oil over the skin. This promotes even browning and helps trigger the Maillard effect for a golden, crispy finish.
Smoke the turkey. Place the turkey in the smoker. Cook at 325°F for about 2½ to 3 hours. Always cook to internal temperature, not time.
Check doneness. Probe the deepest part of the thigh near the hip joint. Pull the turkey when dark meat reaches 165°F. The breast will usually be near 160°F and will finish with carryover heat.
Rest and carve. Tent loosely with foil for 15 to 20 minutes. Carve and serve hot. If serving later, wrap and hold in a clean, warm cooler. Do not reuse the brining cooler unless it has been cleaned and sanitized thoroughly.