Yes you can use your old license plates on your new car and all you have to do is take in some paperwork such as your old registration and your new title and tell the DMV that you want to transfer the license plate to the new car from the old car.
They'll be a fee you have to pay to transfer the license plate to the new car from the old car but it's usually not too expensive and varies depending on the state.
I've transferred old license plates to new vehicles before without a problem and usually have to pay a $20.00 license plate transfer fee.
You can just buy a new license plate if you want too but if your old license plate is okay then you can just transfer the license plate to the new car.