Yes drinking too much Wine can cause you to become drunk.
Wine is an alcohol based drink so it contains alcohol which when you drink too much alcohol your body becomes drunk so while drinking a little wine is okay and you could likely drive after a small glass of Wine you should not drive after drinking 2 or 3 glasses of Wine.
It takes around 1 to 2 glasses of Wine to get a person drunk depending on the persons own tolerance to Alcohol.