If I understand correctly, a rent card is not a payment device. It simply facilitates payment of your rent by acting as a method of identifying you, your landlord, and your rental agreement.
You still need to take cash, a cheque, or a credit or debit card to the shop.
A rent card doesn't "hold" the value of the rent, so you would not be transferring your £150 "onto" the card from your payment source.
The appropriate preposition to use instead of your suggested on or onto would be with or using.