Romney garnered 23 percent of the vote from likely Republican caucus goers, while Bachmann, of Minnesota, attracted 22 percent of the vote, the newspaper reported.
"She's up there as a real competitor and a real contender," Republican pollster Randy Gutermuth told the Register. "This would indicate that she's going to be a real player in Iowa."
Herman Cain, former chief executive officer of Godfather's Pizza, took third place at 10 percent, followed by former U.S. House Speaker Newt Gingrich and Texas Rep. Ron Paul (7 percent), former Minnesota Gov. Tim Pawlenty (6 percent), former U.S. Sen. Rick Santorum of Pennsylvania (4 percent) and former Utah Gov. and Ambassador to China Jon Huntsman (2 percent).
"If I were the Pawlenty camp, I would be enormously concerned about this poll," Jennifer Duffy of the non-partisan Cook Political Report told the newspaper.
Pawlenty has spent more time and resources in Iowa than any other candidate in the election cycle. The Iowa caucuses will take place Feb. 6, 2012.
The poll, conducted by Selzer & Co. Inc., was based on phone interviews with 400 likely GOP caucus-goers June 19-22. The margin of error was 4.9 percentage points.