The bank launched a three-month trial of the technology in Edinburgh yesterday, involving 200 people.
Customers will use the technology to verify payments over £30 - the current contactless card limit - without the need to enter a Pin at the till.
The cards also have contactless functionality and can be used as normal in ATMs, post offices and for digital banking.
To use a card, a fingerprint is registered on to it, which can be done in a customer’s own home. Once a fingerprint is locked on to a card it cannot be changed.
The fingerprint is only held on the card and not centrally by the bank, with each transaction verified using data which is encrypted and stored locally on the card.
Such technology could potentially help people who have difficulty remembering number codes.
Georgina Bulkeley, director of strategy and innovation at RBS, said: “We’re looking to understand from our customers if it’s useful for them, if they like using it.
“Hopefully it will be a really natural experience for them.”
Asked about the potential for a wider rollout, she said: “We really do want to get the customer feedback before we jump ahead.”
David Crawford, head of payments at RBS, said: “We are using the very latest technology across our business to make banking easier for our customers and biometric fingerprint cards are one of the many technologies we are exploring further.
“This is the biggest development in card technology in recent years and it’s great to finally see the cards in the hands of our customers.”
RBS said it was working closely with digital security company Gemalto along with Visa and Mastercard to bring the service to customers in the UK.
Jeni Mundy, Visa’s managing director in UK/Ireland, said: “In financial services, biometrics are gaining ground as a secure and convenient alternative to passwords and PINs. This technology has the potential to make the lives of consumers easier and provides greater choice to confirm their identity. At Visa we’re committed to working with partners to develop and invest in emerging capabilities that deliver a better, more secure payment experience for consumers.”