To deep fry your turkey, you should opt for oil that has a high smoke point. Consider peanut oil which has a smoking point of around 450 F. Almost every recipe will ask you to fry your turkey at 350 F such that the higher smoke point offers a lot of room for any mistakes. If you are someone with peanut allergies, you can consider corn oil. It offers a less flavorful experience as compared to peanut oil but is equally safe and has the same smoke point. You can use canola oil only if you monitor the temperature because it smokes at around 400 degrees. Olive oil, however, is a very bad choice because it has a smoke point of 320 F.