"We can be like friends with benefits, you know?" the driver, named Sandeep Singh, says. He then continued to say that he is willing to pick her up any time she likes.
Horrigan continuously turns down his proposal the entire ride back to her home.
She told the programme that the driver made her feel extremely uncomfortable and that she considered getting out before reaching her final destination.
Singh was confronted by a reporter from A Current Affair and initially denied the sexual requests but, after further conversation, eventually admitted he had made them.
"I would just like to say sorry," Singh told the reporter.
Horrigan was given a full refund for the trip and Singh has been de-registered as an Uber driver.