Can anxiety cause numbness in left side of face feels?

Get it checked: Technically, yes, but so can a variety of other conditions. Please get a physical exam to rule out other possibilities first.

Quite Possible: A variety of symptoms are possible with anxiety, including numbness in the face.

Check it out: If it is something that is unusual and/or bothersome to you, get a physical check up. Anxiety manifests itself in different ways for different people... So yes it is possible. In any case look into treatment for anxiety as well. There are a lot of effective therapies out there. Best wishes.