Barron began his career at Sydney radio station 2GB in 1991, working as a producer for presenters including Malcolm T. Elliott and Clive Robertson, before joining the Macquarie newsroom as journalist and newsreader.
He left in 1996 to resume his studies, before taking a job as a journalist with the Special Broadcasting Service, Grundy Television and later the ABC.
Barron was a presenter on the ABC's NewsRadio network from 1998 to 2012, hosting national programs including the breakfast and drive shows, covering major news stories including the 9/11 attacks on the United States, and presenting The Annual Report - a quiz where listeners had to guess what year events occurred.
Barron has written and presented documentary programs for ABC radio including The Beatles in Australia (2004) and The Day The War Ended (2005), and for television First Stop, Iowa (2008), The Party of Reagan (2012), Madhouse Mess (2013), Fly Me to the Moon (2019), The Bug; Y2K Remembered (2020) and 9/11 Stories (2021).
Barron frequently appears on commercial TV, including The Project, and radio, as an analyst of American politics.