The Gallup poll found 29 percent of Republican voters say they're most likely to support Perry, to 17 percent for Romney, the former Massachusetts governor.
By contrast, before Romney officially entered the race, Gallup's July poll showed Romney led Perry 23 percent to 18 percent. Gallup noted the August poll is its first since the second GOP candidate debate and the Iowa straw poll, which was won by U.S. Rep. Michele Bachmann, R-Minn.
Bachmann came in fourth in Gallup's poll with 10 percent while U.S. Rep. Ron Paul of Texas at 13 percent, with Georgia businessman Herman Cain and former House Speaker Newt Gingrich at 4 percent each and former U.S. Sen. Rick Santorum, 3 percent.
Perry enjoyed strong support -- at or near 40 percent -- among older Republicans and those living in the South, and conservative Republicans strongly favor Perry over Romney, while liberal and moderate Republicans support the two about equally, the poll showed.
With Sarah Palin, the former Alaska governor, and Rudy Giuliani, a former New York City mayor, are still weighing whether to run, the poll showed each receive about 10 percent of the vote when included in the August poll, but if both ran, Perry would still lead Romney 25 percent to 14 percent.
The poll results are based on telephone interviews conducted Aug. 17-21, with a random sample of 1,040 Republicans and Republican-leaning independents. Gallup said it can say with 95 percent confidence that based on the total sample of Republicans, the maximum margin of sampling error is plus or minus 4 percentage points.