Costa attended Annapolis High School in Annapolis, Maryland. After high school he attended Anne Arundel Community College, focusing on general studies.
He defeated Democrat Mike Shay in the 2006 election. In 2002 he defeated Democrat Dotty Chaney to initially capture the seat of this newly created district. Prior to becoming an elected official, Robert Costa served in the United States Army from 1981 until 1985.
After his service in the military, Costa became a professional firefighter with the Anne Arundel County Fire Department.
He has also spent some time as a real estate agent. Costa has been an active member in several organizations.
He is on the Executive Board of Local 1563, the Anne Arundel County Professional Firefighters Association. He was a member Anne Arundel County Republican Central Committee from 1998–2002, serving as its chair from 1999 until 2000.
Finally, he served as the chair of the Board of Directors of the Avalon Shores Civic Association from 1999 until 2001.
He served as Deputy Minority Whip from 2003 to 2005. 2006 Race for Maryland House of Delegates – 33rd District, Division B
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He is also a member of the Italian Businessmen"s Association in Annapolis, the South County Moose Lodge, the Deale Elk"s Lodge, Deale Elementary School Parent Teacher Association, the Alliance of the Chesapeake, the National Rifle Association (National Rifle Association), and the Maryland Rifle and Pistol Association. He is also a member of the Arbor Day Foundation, Citizens for a Sound Economy, and the Anne Arundel Affordable Housing Coalition. While working for the House of Delegates, Costa has been selected as a member of the Health and Government Operations Committee and the Investigation Committee.
Married; 2 children.