Born in Chabás, Aguirre graduated from the youth setup of Arsenal de Sarandí and made his first team debut on 9 November 2008, in a 1–0 defeat against Boca Juniors.[2] On 29 March 2010, he scored his first goal for the club in a 1–0 victory against San Lorenzo. In July, he was loaned to second-tier club Atlético Rafaela.[3]
After amassing more than 100 appearances for Arsenal, Aguirre moved to Lanús on 12 February 2015 as a replacement for the injured Sebastián Leto.[4] On 12 April, he scored his first goal for the club in a 2–1 victory over Banfield.[5] In June 2016, he suffered a muscle injury in his leg, which ruled him out of play for 1 month.[6] With the signing of Miguel Almirón, his playing time became limited in the 2016 season.[7]
On 8 July 2018, Aguirre joined Segunda División side Granada CF, a club also owned by Jiang Lizhang, for one year on a free transfer.[9] He left the club at the end of the season. He remained without club until 19 January 2020, where he signed a deal until June 2021 with Atlético Tucumán.[10]
On 15 September 2021, Aguirre joined Brazilian club Sport Club do Recife.[11] After the move, the club made a mistake and didn't register him, so he couldn't play for the club for the rest of 2021.[12] In February 2021, Aguirre returned to his former club Atlético de Rafaela.[13]