Rodney was born June 4, 1744, at Byfield, his family's farm at Jones Neck, in Dover Hundred, Kent County, Delaware.
Byfield was an 800-acre (3.2 km2) farm where the work was done by enslaved people, and with the addition of other adjacent properties, the Rodneys were, by the standards of the day, wealthy members of the local gentry.
Sufficient income was earned from the sale of wheat and barley to the Philadelphia and West Indies market to provide enough cash and leisure to allow members of the family to participate in the social and political life of Kent County.
Rodney was very active in local politics, as well as the broader range of those elements affecting Delaware as whole.
As early as 1770 he was a Justice of the Peace for Kent County and through the years he held many other local offices.
He was a Colonel in the county's militia, and was involved in a number of actions during the American Revolutionary War.