Is it possible for face numbness and tingling to be a symptom of anxiety?

Yes if bilateral: It is possible. If symptoms are unilateral on face then a more careful neurological examination and probably imaging e.G MRI of brain may be needed.

Anxiety: Yes possible, if accompanied by other symptoms and signs of anxiety.

Anxiety: It is possible but you should consult with your doctor to make sure these symptoms are not caused by a medical condition. If you are cleared medically consult with a mental health professional who specializes in treating anxiety. Remember anxiety is mainly produced by misperceiving situations or interactions. Best wishes.