Yes, I've made pickled turnips many times over the years.
Quick pickled turnips
From Joy of Pickling:
I like using baby turnips, about the size of a golf ball. I'm sure you could use larger turnips & cut them into wedges or cubes.
1 pound baby turnips, trimmed top & bottom & peeled or scrubbed
2 tsp pickling salt
1 cup water
1 tbsp seeded & minced hot pepper
3 tbsp sugar
1.5 cups rice vinegar,
Score each turnip several times at top and bottom. Put the turnips into a bowl. Stir the salt into the water until the salt dissolves and pour this brine over the turnips, Let them stand for 30 minutes to an hour.
Drain the turnips well, retun them to the bowl with the minced pepper and toss well. Combine the sugar and vinegar, stirring until the sugar dissolves. Pour the liquid over the turnips, Cover the bowl with plastic wrap and refrigerate for two days, after which they wiull be ready to eat,
Well covered, they will keep for several months.
I've also made spicy & sour Korean Pickled Turnips, from the same book:
1 pound small turnips, peeled
1.5 tbsp pickling salt
2 tsp korean pepper flakes
3 green onions, minced
8 garlic cloves, minced
1 tsp sugar
Slice the turnips very thinly crosswise. If they are bigger than about 2 inches across, half them lengthwise first.
Put the slices into a bowl and rub them with 1 tbsp of the salt. Let them stand at room temp for about 3 hoursm, occasionally turning them in their brine,
Drain and rinse the turnip slices, and then drain them again. Add the remaining .5 tbsp salt and the remaining ingredients.Pour the mixture into a quart jar nd pour water over the contents so they are covered by about 1 inch. Cap the jar loosely and let it stand at room temperature.
After 6 - 8 days, when the turnips are a sour as you like, cap thr jar tightly.. Store the jar in the fridge, where the pickle should keep for several weeks.
I like them both, but prefer the Korean style.