It really depends more on the maturity level of the child rather than the actual age. Some are ready at 16, some not until much later. You are, of course, not obligated to buy your child a car. It should be seen as a gift, a privilege, rather than something you must or should do.
I suggest when your teen is 16 or 17, buying a car that you allow your teen to use as long as she follows the rules, doesn’t get tickets, or do anything stupid, like drinking and driving. You can let your daughter know that it is her responsibility to check the oil and tires, wash it and keep it clean inside, etc. If she shows that she can be responsible for at least a year with the car, then it becomes hers fully when she turns 18. This is teaching responsibility, which is the most important part of owning a car.