Born in France, Stéphane Da Costa left his native country and moved to the United States to play junior hockey at the age of 17. In 2 years with the Texas Tornado of the NAHL, Da Costa tied for third in team scoring with 23 goals and 40 points.
Da Costa joined Merrimack College of Hockey East in North Andover, Massachusetts for the 2009-10 season. During his first year, he won the National Rookie of the Year, USCHO Rookie of the Year, Inside College Hockey Rookie of the Year, College Hockey News Rookie of the Year, and Hockey East Rookie of the Year.
Da Costa was signed by the Ottawa Senators as an undrafted free agent on March 30, 2011 and made his NHL debut April 2, 2011 against the Toronto Maple Leafs.
In July of 2012, the Senators re-signed Da Costa to a one year contract. Despite starting his season in Binghamton, he was brought back up to the NHL on February 3, 2013 and has registered a goal and an assist in his first 9 games with Ottawa.