Concerns about credit-card security heightened Friday after a little-known Atlanta company disclosed it had been hit by hackers, potentially exposing hundreds of thousands of account holders to fraud.

The breach at Global Payments Inc. is the latest in a wave of data attacks that have heightened consumer concerns about identity theft. The card industry has been particularly vulnerable to those concerns amid a slew of big breaches in recent years as more Americans choose to pay with plastic rather than cash.

The...