Parks made his debut for Costa Rica in a February 1993 UNCAF Nations Cup qualification match against Nicaragua and earned a total of 43 caps, scoring 1 goal. He represented his country in 15 FIFA World Cup qualification matches and played at the 1995 and 1999 UNCAF Nations Cups as well as at the 1993 and 2002 CONCACAF Gold Cups and the 2001 Copa América. Parks was a key member of the national team that qualified for the 2002 FIFA World Cup, serving as the captain. But just before the event started, a knee injury kept him away of participating and he was replaced by Pablo Chinchilla.