The Pew Research Centre study carried out in January showed a sharp increase from mid-2013, when 11 per cent reported being victimised.
The survey also found 21 per cent reported having email or social network accounts compromised, the same percentage as last year.
The findings come amid growing concern over the "Heartbleed" vulnerability discovered earlier this month, and months after US retail giant Target acknowledged millions of customers may have had payment cards compromised.
"Internet users have become more worried about the amount of personal information available about them online - 50 per cent reported this concern in January 2014, up from 33 per cent in 2009."
The report is based on a survey of 1,002 adults from January 23 to 26, including 820 Internet users. The margin of sampling error for the Internet users is estimated at four percentage points.
