Only way to reorganize your cards is to bank your cards by putting them in a trade and having someone cancel the trade. Once they are in the inbox, receive them in the order you want them to appear in your units list. This is especially important when you want to organize your monster defense.
I have to say, this is a STUPID aspect of the game. If you're going to make a cap on how many units we can have, at least make it so that we can send cards to the inbox. It's quite frustrating having to bother my allies with banking.