Born in Las Cruces, New Mexico, Barraza is of Mexican descent and spent his early career with the Real Salt Lake Arizona academy.

[5] On January 11, 2019, Barraza was selected with the 12th overall pick at the 2019 MLS SuperDraft by New York City FC.

[2] On December 15, 2020, almost two years since signing his professional deal, Barraza made his professional debut for New York City in a 4–0 loss against Tigres UANL in the CONCACAF Champions League.

[6] On May 31, 2021, Barraza moved to USL Championship side Oakland Roots on loan.

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