The 23-year-old centre from Paris, France has nine goals and 15 assists in 31 games with the Binghamton Senators. This is Da Costa's first recall to Ottawa this season.
Da Costa was originally signed by the Senators as an undrafted college free agent on March 31, 2011, after two NCAA seasons with Merrimack College.
In 26 career NHL games, he has scored three goals and two assists.
He has represented his native France at each of the last four IIHF world championships.