In August 2008, he made his official debut in a 2–0 victory against Sport Boys in Matute, playing the entire game and doing an outstanding performance.

In December 2016, he was signed by Universitario de Deportes with a contract for two seasons, in which he played in the qualifying stages of the 2017 and 2018 Copa Libertadores.

Corzo was part of the Peru U-20 team in the 2009 South American Youth Championship, being eliminated quickly by losing four games.

On 2 February 2009, he was called to the senior team by the then current coach Jose 'Chemo' del Solar to play a friendly against El Salvador losing 1–0.

[4] In June 2011, the new Peruvian national team coach Sergio Markarián decided to give Corzo a chance to play in a friendly against Senegal.

Corzo's performances with Municipal made manager Ricardo Gareca call him up for Peru's squad for the Copa América Centenario, where he played in 2 out of 4 matches.