Will surgery cure the numbness on my face caused by an orbital fracture?

No: Most likely not. Numbness is most likely due to involvement of the infraorbital nerve, which provides sensation to the front part of your cheek. Depending on when your injury took place, will most likely resolve with tincture of time, though some folks will always have some area of numbness.

Not likely: Usually the facial numbness is caused by injury to the nerve as it exists the facial skeleton. This exit point is a weak spot and the bones often break there, damaging the nerve. There is actually a small risk of nerve injury with surgery. Generally, if the nerve is not torn or cut, it will regain sensation very slowly over 6-8 months. Best wishes.

It is possible : If a nerve was trapped and injured in a fracture line then decompressing the nerve can help. In my 22 years of practice I have had 3 patients who were helped by this procedure. All 3 had mid face fractures involving the infraorbital nerve with facial and dental numbness.

Possibly: It all depends on how severe the fracture is. Almost all orbital fractures have some numbness since the nerve that give feeling to your face runs inside the weak orbit floor bone right where the fracture often is. In the large majority of people this numbness will slowly go away. Surgery may or may not help this - discuss it with your surgeon.