WARNING, THIS WILL, 100% GUARANTEED, NET YOU A PERMANENT BAN! USE ONLY ON A THROWAWAY ACCOUNT!!
You have to be on NA server,
Go to purchase RP make sure payment method is on USA. (You can change that on the bottom)
Click mobile payment.
Click 10 dollars.
Enter this number: 7043490979
It says enter pin:
Just wait for 10-30 seconds.
It shall give you an error.
Click on the button that says something like continue or close i don't remember.
You shall have your RP enjoy.
Original thread: Unlimited RP Method, Here Ya Go - General Discussion - Bot of Legends
EDIT: Since they "nerfed" this already (max 3 RP purchases per day), you can only get around 4k RP per account. I've found that making an account, getting the 4k RP, and then buying champions I've wanted to try but don't want to spend IP/RP on just in case I don't like them a very good use of this.