Arguelles was the second Latino to serve on California's high court and was one of the founding members of the Mexican American Bar Association of Los Angeles.
He was appointed by Governor Pat Brown as a Judge of the East Los Angeles Municipal Court, serving December 4, 1963 – September 19, 1969.
[8] In 1969, Governor Ronald Reagan appointed Arguelles as a Judge of the Los Angeles Superior Court, where he presided for nearly 15 years from September 19, 1969 to May 14, 1984.
[8] In 1984, Governor George Deukmejian elevated Arguelles to Associate Justice of the California Court of Appeal, Second Appellate District, Division 4, where he served May 14, 1984 – March 18, 1987.
[8][11][12] Following his court service, he became counsel to the law firm of Gibson, Dunn & Crutcher, and also served as an arbitrator and mediator.