'Face pain' is a little too broad a description to be able to give you a specific answer. A traditional acupuncturist would ask you the same sorts of question that your doctor would - where is it, what kind of pain, what times of day does it come on, what makes it better or worse, and so on. Because the acupuncturist works within a different framework the strategies they decide upon will be different, but will always be based on an underlying premise that pain arises from blockages, excesses or deficiencies in the body's energy which the needles are used to correct.
A great deal of the early research in the west was around the pain relieving qualities of using needles, and even the most hardened sceptic had to admit that people did seem to have less pain after treatment. The question is only how much relief from pain and how sustainable it is, and if you did go to see an acupuncturist you'd be well advised to set clear outcomes and regular review periods.
Our factsheets on the main website (click on 'research', then 'factsheets', and look at the drop down menu) gives you an idea of the sorts of research which exists for the kinds of problems which people regularly bring to acupuncture treatment.