His consistent performances convinced Markarian to include him in Peru's squad for the 2011 Copa América. He made his Copa America debut by starting against Chile in the group stage. Despite the loss, Corzo put in a strong performance at left back by not allowing Chile, with Alexis, to score. His second game in the Copa America was against Venezuela in the third-place match. Corzo again played from the start of the match and gave another solid performance this time at right back. In the end, he helped Peru claim the Bronze medal by winning the match 4–1. This is (coupled with the 2015 Copa América) Peru's best result in the Copa America since they last won Gold in 1975.