"I did not vote for any incumbent. Any incumbent I want out. We need change, period," resident Rickie Eadens told ABC News.
Another voter, Brad Leix, said he voted for Paul because he is not a Washington insider.
"I'm just tired of the government insiders. You've got certain people who've been in office for so long. We need some outside views that aren't afraid to rock the boat a little bit. So, I think that people like him will be good for the country," Leix said.
A spokesman for the Kentucky Secretary of State's office told ABC News that turnout was low and absentee voting was down 16 percent from the previous primary.
Kentucky's liberal Attorney General Paul Conway, won the Democratic nomination. Conway was running against the more conservative Lt. Gov. Dan Mongiardo, who opposed President Obama's health care plan.
ABC News' Andrew Fies contributed to this report.