The article in GQ quotes an unnamed woman as saying Rand Paul and a friend once blindfolded her, tied her up, drove her to their house and tried to force her to smoke marijuana. The woman said she and Paul were teammates on the Baylor University swim team at the time, about a quarter-century ago.
In an interview with Fox News, Paul did not directly answer when asked about another detail in the article attributed to the woman - that he and his friend drove her to a creek, where they told her their god was "Aqua Buddha" and she should bow down to him.
"To produce someone anonymously, and then I'm supposed to somehow respond to an anonymous person from 27 years ago, who in the end says - whoever this person was, says - we didn't do any harm to them and it was all in fun and we didn't do anything wrong - and yet it's being characterized as kidnapping, it's kind of a craziness," Paul said.
"But the thing is, is we used to have journalist ethics in our country, that you wouldn't report something from one anonymous source, particularly accusing somebody of something like that. It's so ridiculous, I don't know where to start," he said.
Asked whether the incident could have been playful fun, he replied, "I think I would remember if I'd kidnapped something and - someone - and I don't remember and I absolutely deny kidnapping anyone ever."
Jim Nelson, GQ's editor in chief, defended the story in a statement issued before the television interview. "We stand by the story, and we gave the Paul campaign every opportunity to refute it. We notice that they have not, in fact, refuted it," he said.
Paul used the issue to raise money. In a letter posted on his campaign website, he asked supporters to contribute so that he can beef up his staff and to pay for political ads.
"It's become very clear you and I will NOT be able to count on anything approaching a fair shake from the media," he wrote. "So we're going to have to go around them."
In a radio interview with Sean Hannity, Paul angered parishioners at a small-town Kentucky church by saying he and other politicians who attended its fundraising picnic had to worry about having beer thrown on them. The picnic does not serve alcohol as it's in a dry area.
"We were in a place called Fancy Farm, which is just a wild picnic where they boo your entire speech. And it's a very partisan thing, and you do worry about people throwing beer on you and throwing things at you," Paul said.
Parishioner Mark Wilson at St. Jerome called for Paul to retract the unflattering comments, fearing they would discourage families from attending.
"We have never known of any objects being thrown, and especially we've never heard of any problems with beer being thrown," Wilson said.