A small amount of barefoot running each week will strengthen your feet.
You need three things to minimize your risk of twisting an ankle when running off-road: stronger foot and ankle muscles, better balance and improved proprioception, or body awareness.
The simplest way to strengthen your foot muscles and some of your ankle stabilizers is to do a small amount of barefoot running each week. About 20 minutes of unshod jogging on grass or your home treadmill will do the trick.
To improve your balance and proprioception while also strengthening your ankle stabilizing muscles, try pillow balancing. Place a bed pillow on the floor and stand on it with one foot. Try to go for 30 seconds without touching your other foot down. If that’s too easy, try it with your eyes closed or stack pillows. One minute per foot every other day or so is plenty.
Balance boards such as the Fitterfirst Softboard or Indo Board are also great tools for training balance, proprioception and strengthening the ankle musculature. Time how long you can stay balanced on your board, and aim to improve your personal best every other day.