There have been many proposals to do something like that. There is a proven way to use something called digital cash using public key encryption.

Digital cash allows you to send a long number which represents a single payment and can only be used for that single payment. Thus if the number represents you paying $100 to priceline.com, it can only be used for a single transfer of 100. If someone else tries the same number again, the bank will say, sorry this one has already been used up. In addition to being secure this system can provide absolute privacy.

So theoretically, it is possible but it has not happened. I think one reason is that credit card companies like having people's personal information and being able to see all their purchases.