You can drive a motorcycle with a car license if your car license has a motorcycle endorsement on it.
So you would have to take a motorcycle test and get licensed to ride a motorcycle with your car license.
Some states may give you a separate motorcycle license that is different from your car license.
If your car drivers license has no motorcycle endorsement then no you cannot legally drive or ride a motorcycle with your car license.
You have to take a separate test which is a motorcycle written test as well as a test of you driving the motorcycle before you can get a motorcycle license.
Getting a motorcycle license is pretty easy though and you can get one through your DMV.
Make sure you study up on the laws on motorcycles before you take the motorcycle written test.