With all but nine of the state's 1,774 precincts reporting early Wednesday, the unofficial results had Santorum with 29,968 votes to Romney's 29,964, The Des Moines Register reported.
Santorum, a former U.S. senator from Pennsylvania, told his supporters the country needs "bold ideas, sharp contrasts and a plan that includes everyone" and puts people to work.
"I also believe we, as Republicans, have to look at those who are not doing well in society," he said.
The Washington publication Politico reported Santorum, when asked if he had a message for Romney, repeated the first words of his speech: "Game on."
Santorum's surge to the top of the Republican field alongside Romney was "absolutely incredible," supporter Chuck Laudner of Rockford said.
"What could top this? I hate to see this circus leave town because you want to capture this thrill," the former executive director of the Iowa Republican Party told the Register.