Not unless you have a contract with them. It is NEVER a good idea to use your own car for work. It's up to a company to either have a contract with you and pay your gas, some mechanical bills, etc. Many smaller companies will take full advantage of someone using their car. EXAMPLE: Using your car to deliver Pizza, packages, etc. If the ad in the paper or in your interview the Manager told you, you would need to use your car and you agreed then you are out of luck.
Marcy
The above answer is also correct. As an addition to that, if you are using your car for business purposes, and have not told your insurance company this, they could cancel your policy or raise your rates. Vehicles used for business purposes are usually charged a higher insurance premium due to higher miles driven.