Born to Scottish immigrants in Dutchess County, New York, McArthur grew up in western Pennsylvania and later moved to Kentucky, where he was employed as an Indian ranger. McArthur moved across the Ohio River in 1797 to the new town of Chillicothe, Ohio, which was to become the state capital in 1803. McArthur grew wealthy investing in land in the surrounding area. He was elected to the United States House of Representatives while serving in the militia during the War of 1812, but never qualified for office, preferring to continue serving in the military. He was appointed a Brigadier General in the U.S. Army shortly thereafter and was placed in charge of the Army of the Northwest after William Henry Harrison's resignation. He did not face much action but was instead engaged in negotiating treaties with the Indians. McArthur served intermittently thereafter in the Ohio House of Representatives and Ohio State Senate, as well as a single term from 1823-1825 in the United States House of Representatives before winning election to the governorship in 1830. McArthur served a single term and did not seek re-election.
After the death of Duncan's mother when he was three, his father remarried and, in 1780, moved his family to western Pennsylvania.
For the next two years McArthur was employed by the state of Kentucky as an Indian ranger to patrol the Ohio River.
McArthur's first important public office was that of representative from Ross County in the Ohio General Assembly, to which he was elected in the fall of 1804.