Robert Smith was born in Lancaster, Pennsylvania, on November 3, 1757, and graduated from Princeton University. He began his professional career as a private in the Continental Army, volunteering in 1781 and serving through the end of the Revolutionary War. Smith soon moved on to the field of law, and established a prominent admiralty practice in Baltimore, Maryland, between the years of 1783 and 1793. In 1793, he won a seat in the Maryland State Senate and served until 1795. He continued in state politics, serving in the Maryland House of Delegates, and then spent three years as a member of the Baltimore City Council (1798-1801).In 1802, President Thomas Jefferson chose Smith as secretary of the Navy to complete his first presidential cabinet. Jefferson's decision followed the recommendation of Smith's brother, Senator Samuel Smith, who had been Jefferson's first choice for the job. Robert Smith served as secretary of the Navy until 1809, when James Madison replaced Jefferson as President of the United States. Upon Madison's arrival, Smith became the President's secretary of state.

Disagreements on policy, however, cultivated an intense enmity between the two men, eventually resulting in Smith's resignation in 1811. Smith retired from politics after his time in Madison's cabinet and died in Baltimore, Maryland, on November 26, 1842.