The Pew Research Center study carried out in January showed a sharp increase from mid-2013, when 11 percent reported being victimized.
The survey also found 21 percent 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.
"As online Americans have become ever more engaged with online life, their concerns about the amount of personal information available about them online have shifted as well," the Pew researchers wrote.
"Internet users have become more worried about the amount of personal information available about them online -- 50 percent reported this concern in January 2014, up from 33 percent 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.
NJF/NJF