What legal action can I take against a person who’s in a different state that received a loan from me but now refuses to pay it back?

If there was an agreement to repay you--i.e., you can show that the money or payment made (using your credit card) on that person's behalf was not a gift--you could sue for the money's return. You may do so even if the agreement to repay was oral; oral agreements are enforceable, though as practical matter, it is more difficult to show the existence and terms of the agreement if the other party to it "remembers" things differently.

You should be able to sue in your own local courts, since the court where someone suffered financial injury should have jurisdiction. That's the good news. The bad news is:

1) I don't believe you can sue an out-of-state defendant in small claims court; you'll need to go the regular county court, which is more expensive and more complicated than a small claims action.  Between that and the additonal complications of suing an out-of-state defendant, you may effectively need  an attorney (rather than representing yourself, as you could easily do in small claims), which may mean that it is not cost effective to sue.

2) If you sue and win but your friend does not pay, you'll have to then enforce the judgment in his or her home state or where he or she owns property. As with suing an out-of-state defendant, enforcing judgments against out-of-state defendants is more time consuming, complicated, and often expensive, too.

Depending on how much is at stake, even though you legally could sue, it may not be worth it.