Half of my tongue is numb after wisdom tooth extraction, is this normal?

It happens: After the extraction of a lower wisdom tooth, there can be some lingering numbness. This usually means the roots of the extracted tooth were very close to the inferior alveolar nerve which runs the length of the lower jawbone. Often the feeling will come back. Sometimes it doesn't and that is one of the unfortunate rare side effects of wisdom tooth extractions. See your dentist or oral surgeon.

Paresthesia: I assume that you had a lower wisdom tooth removed and that the doctor who removed your tooth gave you an injection of a local anesthetic to numb the tooth. That injection also numbs the tongue on the same side. If the doctor accidentally hit the nerve during the injection, or traumatized the nerve during tooth removal, the tongue may remain numb for a while. Eventually, all feeling will return.