Marchena made his debut for Costa Rica in a February 1987 friendly match against South Korea and earned a total of 48 caps, scoring no goals. He represented his country in 13 FIFA World Cup qualification matches and was part of the national team squad, that played in the 1990 FIFA World Cup in Italy, and featured in all four games played. He also played at the 1991 UNCAF Nations Cup and the 1991 CONCACAF Gold Cup.