Yes, but there are security concerns that you will need to address.
You need to either avoid storing credit card numbers after the transaction has been processed or to encrypt that data. There are plug ins you can use to encrypt data or FileMaker 13 or newer can be used to encrypt the entire file.
There are plug ins that facilitate processing the credit card transactions. You will need to select one and evaluate it carefully in terms of how securely they manage the transactions.
Thanks for the assist Stacy and Phil. This will get me started. I do not really want to do this. But, I need to research the alternatives. The credit card processors on the 360works item were not the ones we use. So I need to research if they are compatible. As always thanks for speedy replies