Legal Question in Business Law in California

That depends on what your arbitration agreement says. That agreement is probably part of your overall contract with the credit card company but could instead be a separate document.

The arbitration agreement is indeed the starting point. However, it may merely state that the arbitration shall be under the rules of some particular organization, such as the American Arbitration Association. In that case, you'll need to go on line and look up how arbitration is handled under that organization's rules.