The poll, released Monday by Quinnipiac University in Hamden, Conn., found 36 percent of likely voters said they support the former senator from Pennsylvania, who had strong support among men and conservatives, compared with 29 percent for former Massachusetts Gov. Mitt Romney.
The poll showed House Speaker Newt Gingrich of Georgia followed with 17 percent and U.S. Rep. Ron Paul of Texas with 11 percent of likely voters in the March 6 primary.
But the poll found 45 percent of likely voters said they may change their mind.
Among men, 38 percent said they backed Santorum to 25 percent for Romney, while 34 percent of women said they supported Santorum to 33 percent for Romney.
For respondents who described themselves as conservatives, 40 percent said they backed Santorum to 25 percent for Romney.
Among Tea Party members, 49 percent said they supported Santorum to 19 percent for Romney, while those who described themselves as moderates said they supported Romney over Santorum, 39 percent to 27 percent.
Quinnipiac University surveyed 847 likely Ohio Republican primary voters Thursday through Sunday. The poll has a margin of error of 3.4 percentage points.