Borges has earned a total of 133 caps for the Costa Rica national football team, scoring 23 goals. He has represented his country in 35 FIFA World Cup qualification matches and at the 2014 and 2018 FIFA World Cup finals. He has also played at the 2011 and 2013 Copa Centroamericana, as well as at the 2009, 2011, 2013, 2015 and 2019 CONCACAF Gold Cups, and the Copa América Centenario.