Can general anesthesia cause numbness to face and tongue?

Not typically: It would be unusual for numbness of the tongue to arise just from general anesthesia unless the anesthesiologist was exceptionally agressive during intubation and did significant damage in the mouth. Numbness in the face would also be very unlikely.

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.