Acosta made his professional debut for
Santos de Guápiles in the 2004/05 season and left them in 2010 for
Alajuelense with whom he won three league titles. In January 2013, he moved abroad to have a six-month loan spell at Mexican second division side
Dorados. On 8 September 2016, Acosta joined
Herediano. On 29 November 2017, he renewed his contract for another year. On 10 January, he switched to Colombian club
Rionegro Águilas.
East Bengal On 11 July 2018, Acosta joined Indian club
East Bengal Club for a fee of . He was issued the number 2 jersey. On 2 September, he made his debut for the club and scored a goal in a 2–2 draw against
Mohun Bagan in the
Kolkata derby at the Salt Lake Stadium in
Calcutta Football League. On 16 April 2019, he left the club. On 26 June 2019, Acosta signed with Costa Rican club
UCR. On 6 March 2020, he returned to East Bengal until the end of the season as a replacement for Liberian
Ansumana Kromah. ==International career==