The Pew Research Center for the People & the Press said former U.S. House Speaker Newt Gingrich placed second in its poll of 1,207 registered voters, including 527 Republican and Republican-leaning independent voters, with 16 percent, followed by Ron Paul at 15 percent and Rick Santorum with 14 percent.
The poll, conducted Jan. 11-16, showed Romney's overall appeal has declined from 38 percent in November.
In a general election matchup, Romney came in second to President Barack Obama with 45 percent. Overall, 50 percent of those polled said they would vote for Obama.
If Paul chose to run for president as a third-party candidate, 18 percent of those polled said they would vote for him, while 44 percent said they would vote for Obama and 32 percent said they would back Romney.
The Pew Research Center poll has a margin of error of 3.5 percent.