Remove the turkey from the brine, and pat dry with a paper towel. Place, uncovered, into a refrigerator for 2 hours to allow the skin to dry.
Preheat smoker to 250 degrees Fahrenheit using a fruit wood, like cherry or apple. While smoker comes to temperature, remove the turkey from the fridge and coat in olive oil, and season liberally with dry rub.
Smoke the turkey for 2 - 3 hours, depending on the size of the turkey breast, or until the internal temperature of the turkey is 160 degrees F.
In a small bowl combine maple syrup and orange juice. When the turkey reaches 160 degrees brush the turkey breast with the maple orange combination. Remove the turkey from the smoker and let it rest for 15 minutes.
Slice and serve with your smoked gravy or favorite topping.