After his education, Riggs moved to Georgetown, DC, where he was employed as a merchant. He fought in the War of 1812 as an ensign in the 32nd regiment of militia in Anne Arundel County, Maryland. Before that, he had established himself as a dry goods merchant and hired George Peabody as his office-boy.
By 1815, Riggs and Peabody entered into a partnership under the firm name of Riggs & Peabody, dry goods merchant. Business flourished and soon they expanded to Baltimore in 1816. By 1821, they had offices in New York City and Philadelphia. In 1822 the firm’s name was changed to Riggs, Peabody & Co. with the main office in Baltimore. In 1829 the partnership was dissolved and Riggs retired to New York City. His estate is now part of the United States customs house.
Riggs and Peabody continued their business ventures and engaged in international finance. They were mainly concerned with restoring the credit of Maryland abroad after the depression of 1841-1842 and disposed a bond issue of $8 million. Before moving to New York, Elisha established the bank of Corcoran & Riggs in Washington, DC, which was organized by his son George Washington Riggs and financed by Elisha. When the United States sought a loan to finance the Mexican-American War, the Riggs bank was the only institution to bid for the full amount and lent the government $34 million in 1847 and 1848. After the retirement of William Corcoran, Elisha's son George Washington Riggs and his grandson Elisha Francis Riggs took over the business as Riggs & Co. in Washington. It was successfully run as such until July 1896 when it assumed its present name as the Riggs National Bank. The bank still stands at its original location.