There are reasons why acne may be able to be treated with apple cider vinegar. But it is important to bear in mind that not everything is going to work for everyone. That noted, if consumed (drank) apple cider vinegar does increase glucose tolerance and decreases insulin resistance. So due to that, it may be able to in turn regulate the hormones that trigger acne breakouts. Second off, sometimes it helps with compromised intestines by changing their bacterial makeup. This can cause other bacteria that cause acne to be gone.
It is not recommended for long term use orally because it is good at stripping the enamel off of your teeth due to its high acidity. This is besides the fact that it just tastes horrible and nothing normally works without consistent use; which is difficult to do because of its taste.
It does make more sense to use this topically; as in rinse your skin off with it after washing it. It does have similar effects for different reasons as the method of use is different. Thing is, it still only works as long as you are using it; which in my book makes it a bandaid solution.
In short, if you are desperate and there is not much at the house, you can give this a try; but I would not recommend apple cider for acne long term treatment.