Is it possible for general anesthesia cause numbness to face and tounge?

Not really: General anesthesia sometimes involves a breathing tube or airway device that may cause numbness to the tongue but not the face.

Highly unlikely: The anesthesia itself shouldn't cause the numbness, but local anesthetics (commonly referred to as "novocaine") or surgical procedures can result in numbness.

Yes: This is however, not due to the anesthesia, but is more likely due to the manipulation of the airway. More specifically this is most likely due to having a breathing tube placed during the surgery. This usually resolves fairly quickly. The facial numbness is more concerning and i would ask that you speak to your anesthesiologist.