Before moving to Deportivo Saprissa in Costa Rica, Arrieta played for Guanacasteca and their successors Brujas. While with Saprissa, Arrieta scored 48 goals in 178 league matches. He also played an important part in Saprissa's Costa Rican league titles in 2006–07, 2007-08 Apertura, 2007-08 Clausura, 2008-09 Apertura, and 2010 Clausura.
In April 2012, Arrieta signed a two and a half-year agreement with the Columbus Crew, moving to play outside of Costa Rica for the first time in his career. It was officially announced on 26 April 2012 that Arrieta had signed with the Columbus Crew of Major League Soccer. Arrieta made his MLS debut for the Crew on 14 July, playing 62 minutes in a loss to Sporting Kansas City at home. This came just 17 days after the 27 June transfer window opened. Two weeks later, in a rematch at Kansas City, Arrieta scored his first MLS goal in the 17th minute of the match, following with the game winner in the 34th minute. After only his third game in MLS, Arrieta was named League Player of the Week with a 2 goal performance in a Columbus win against Sporting Kansas City.