After measuring the amount of oil needed for the deep-fryer, dry the turkey well, inside and out, before proceeding.
Mix the smoked paprika, salt, garlic powder, black pepper, onion powder, cayenne pepper, and thyme together in a bowl. Sprinkle the spice rub inside the cavity of the turkey and on the skin. Separate the skin from the breast meat and massage the rub onto the meat with your hands. Put the turkey on a large sheet tray and cover with plastic wrap. Refrigerate overnight or up to 24 hours.
Fill the electric deep-fryer with peanut oil and preheat to 400 degrees F, (it will take about 1 hour for the oil to come to temperature).
Remove the turkey from the refrigerator and let it come to room temperature.
Once the oil is hot and the turkey is at room temperature, very carefully lower the turkey into the hot oil. Make sure the oil maintains its temperature while frying. Fry the turkey until the skin is dark golden brown and crisp, or until the internal temperature of the breast reaches 155 degrees F on an instant-read thermometer, roughly 45 minutes. Carefully remove the turkey from the oil and let it rest and drain on a wire rack, about 30 minutes. The internal temperature will rise to 165 degrees F while resting.
Transfer the turkey to a serving platter and serve.
To measure the amount of oil needed to fry the turkey, put the turkey in the fryer, add water to top of turkey, and mark the water line with a crayon or marker. Remove the turkey and the water line will indicate how much oil will be needed to fry your turkey. Having too much oil can cause a fire. The pot should not be more than 3/4 full or the oil could overflow when the turkey is added. Dry the fryer before adding the oil.