Parra began playing football with the youth system of Pachuca.[1] In 2014, he joined the youth system of Monterrey.[2]
Club career
On 14 August 2016, Parra made his debut for Monterrey, in a CONCACAF Champions League match against Don Bosco.[3] On 14 August 2016, he made his Liga MX debut coming on as a substitute in the 89th minute for Celso Ortiz in the 2-1 victory against Necaxa.[4] In 2019, he began his first full senior season, however, his progress was interrupted by knee injuries to both knees, that kept him out of action for a year and a half, prompting the club to pursue loan options upon his return.[5] In 2021, he played with the second team, Raya2 Expansión, in the second tier Liga de Expansión MX.[1] In May 2022, he went on loan with Necaxa in Liga MX.[6][7] In November 2022, he joined Atlético Morelia in the second tier Liga de Expansión MX on loan.[8] In June 2023, he departed the club to return to Monterrey, after having finished as the team's leading scorer with four goals, despite playing as a fullback.[9][10] In March 2024, he went on full-year loan with Forge FC of the Canadian Premier League, with an option to extend it for an additional year.[11][12] He made his debut for Forge on 13 April 2024, against Cavalry FC.[13]
International career
In September 2014, Parra was called up to a camp with the Mexico U17 team.[14]