Can I sue the car dealership if I had a car accident and the air bag did not deploy which got me injured?

How did the car dealership act negligently when there was no reason for them to think the air bag might not deploy properly? Your suit would be against the manufacturer of the airbag and perhaps the maker of the car. There are attorneys who handle such cases and you should speak to them to see if you have a case and whether your damages [you don't say what injuries occurred] justify a suit or even settlement demand.