Anchia is an Attorney with Haynes and Boone, LLP. He has worked as an Attorney for Patton Boggs LLP, as a guest lecturer at Saint Mary's University School of Law, Adjunct Professor at Texas Technical University Law School, and visiting Professor at Tulane University School of Law.

Anchia is a member of Catholic Campus Community - Southern Methodist University, Dallas Assembly, Leadership Dallas Alumni Association, Oak Cliff Lions Club, Southern Methodist University Clements Center on Southwest Studies, and Chair of the National Association of Latino Elected and Appointed Officials.