Born in Montevideo, Acosta joined Centro Atlético Fénix's youth setup in 2009, aged 13.
[1] Acosta scored his first professional goal on 16 February 2014, netting the second in a 3–0 away win against Racing Club de Montevideo.
[5] On 15 January 2018, Acosta joined Segunda División B team Racing de Santander on loan until the end of the season.
[7] He left Villarreal at the end of 2019 and remained without a club until 10 August 2020, when he signed with Atenas de San Carlos.
On 6 March 2021, a day after his 25th birthday, Acosta disappeared after trying with his brother to swim across the Arroyo Pando, located in the Department of Canelones, Uruguay.