The best I could come up with is "smart card reader". However, that seems to be a device that reads all kinds of things, even cards for health care coverage and the likes. (Wiki says the following about smart cards: Smart cards serve as credit or ATM cards, fuel cards, mobile phone SIMs, authorization cards for pay television, household utility pre-payment cards, high-security identification and access-control cards, and public transport and public phone payment cards.)

Is there a more specific term for a reader for bank cards?