Rinse the turkey legs and pat them dry with paper towels. Rub them all over with olive oil.
In a small bowl, mix the salt, black pepper, smoked paprika, garlic powder, onion powder, thyme, oregano, brown sugar, and cayenne pepper. Coat the turkey legs evenly with the seasoning blend, making sure to get into all the creases.
Cover and refrigerate the seasoned turkey legs for at least 2 hours, or overnight for deeper flavor.
Prepare your smoker to 250°F (120°C). Add the soaked wood chips to the smoker and place a pan of water or apple juice inside to keep the meat moist.
Arrange the turkey legs on the smoker grates, leaving space between them. Smoke for 2½ to 3½ hours, turning once halfway through, until the internal temperature reaches 165°F (74°C) and the skin is dark and smoky.
Remove from the smoker and let rest for 10 minutes before serving. Serve hot with coleslaw, baked beans, cornbread, or potato salad.
