Democrats trounced Republicans 22-0 during the game earlier this month, due in part to the pitching of Rep. Cedric Richmond (R-La.), who played college ball.
Paul joked that, since Democrats "love regulations," they should pass some to make the game easier for Republicans, who have lost the past five games.
"I said, Democrats, look, you guys love regulations so much? Why don't we pass a regulation that says your pitcher can only pitch for two innings?" he said to laughter from the crowd. "So far we haven't gotten any word back from them on that."
He also suggested Democrats, because they "like equality of outcome," would be amenable to giving Republicans six outs per inning.
"So I also have asked them, it's like, you guys like equality of outcome, right? So maybe we need to get six outs per inning. And if you all score six runs, why don't you give us six runs, just to be fair," he said.
Paul added: "So far they're for dog-eat-dog capitalism when it gets out on the baseball field."
The baseball cracks were the opening to a well-received address Paul gave Friday to a South Carolina GOP barbecue during a visit to the early primary state.
He later veered onto more serious topics, suggesting President Obama was "losing respect" with the public for predicting catastrophic effects from sequestration that never materialized, and asserting that former Secretary of State Hillary Clinton hadn't told the truth when testifying to the Senate on the attacks on Benghazi.
Paul is considered to be a likely 2016 presidential contender, and his visit to the state allowed him to gauge support for a potential bid.