Craig was born in Orange County, Virginia in approximately 1738. He was ordained a Baptist minister in 1771, and was imprisoned briefly in South Carolina, apparently for disturbing the peace with his sermons. He then moved to what was then Bourbon County, Kentucky and settled in the area of Frankfort, Kentucky in 1785. In 1777, he became pastor of Blue Run Church.
Craig was a shrewd businessman and a local magnate; he built the first fulling-mill and the first paper-mill in Kentucky as well as the distillery he founded in approximately 1789 in Georgetown, Kentucky. A recurring, if probably unverifiable legend credits Craig's distillery with being the first to age corn whiskey in new charred oak barrels, which is the decisive step in turning white lightning into Bourbon whiskey.
Craig died in Georgetown in 1808. His firm ultimately continues as Heaven Hill Distilleries.