Always read that fine print with the credit card companies. You could be limited in what you can xfer and also the APR could change depending on their policies.
Putting the car loan on your credit card could affect you negatively in a few ways.
Having a debt like a car loan, or mortgage looks better on your credit report than a high revolving credit card balance.
If the transfer amount to the credit card is close to your total credit limit (on top of it being a long standing revolving balance), then that looks worse on a credit record.
Your car loan is a lump sum loan at a certain dollar amount, amortized over the life of the loan, it's not a line of credit, so you have more security knowing that loan is locked in until the principle is completely paid off, you don't have anywhere near such security with a credit card line of credit.
If something happens in your life and you cannot pay the loan off, then you are in better standing with a lein on your item, rather than an outstanding and revolving line of credit. If the bank wants to repossess the car and close the loan, you're in better shape than if you outright own the car and have an oustanding credit card balance. The bank knows it's money is tied to a tangable asset, the credit card company does not, and only knows that you owe them X amount of dollars for whatever reason.
I guess it could depend on your situation, but I don't think it's an overall good idea.