The campaign, by the radio specialist Eardrum, involves two ads, which will run in rotation. The first is a straightforward promotion, while the second takes a different tack, saying the film "misrepresents" the country's leaders.
The campaign was written by Ralph van Dijk, Eardrum's managing director and co-founder. "All too often, radio ads underestimate the listeners' intelligence - this campaign forces them to think," he said.
Danny Perkins, the head of releasing at Optimum Releasing, the film's UK distributor, said: "A lot of people in the US have made great efforts to discourage people from seeing the film."
The campaign also includes print work featuring Moore and President Bush in front of the White House. It will run in titles such as Time Out.