Smoked turkey brine is made by covering a turkey in a mixture made of water, salt, sugar, tarragon and black pepper before smoking it. The water for the brine should not be chlorinated. If it is, boil the water first before making the brine mixture.
To make 1 gallon of brine, mix 1 gallon of water, 1 cup of salt, 1 cup of sugar, six fresh tarragon leaves or 1/4 cup dried tarragon, and 1 teaspoon of black pepper. Place turkey in a non-metallic dish and cover completely with brine mixture. Place the turkey, still covered in the mixture, in the refrigerator and let it sit for one hour for each pound. When the turkey is done marinating, remove it from the brine mixture, rinse it thoroughly and then coat it with olive oil. The turkey is then ready to be placed in the smoker.
Smoking the turkey requires about 30 minutes of smoking per pound at 235 degrees Fahrenheit for smaller turkeys, and 25 minutes per pound at 250 degrees Fahrenheit for larger turkeys. It is better to smoke turkeys weighing 20 pounds or less. Place a pan under the turkey with 4 cups of water to catch the drippings and prevent the drippings from drying out and burning.