Expect to cook turkey drumsticks for anywhere between 90 to 110 minutes. The total weight of the turkey legs doesn't affect their cooking time, unlike a full turkey. Check their internal temperature at regular intervals with a meat thermometer. When the temperature reaches at least 165 degrees Fahrenheit, they're finished cooking. You can wait a little longer for them to cook if they don't look finished at 165 degrees Fahrenheit, but don't cook them past 170 degrees Fahrenheit.