Ordorika majored in physics at the Facultad de Ciencias in the in 1991. It is during his student days in the 1980s that he became a militant of the Mexican revolutionary left (izquierda revolucionaria) through the Comité Estudiantil de Solidaridad Obrero Campesina (CESOC) and as a member of Revista Punto Critico, a marxist organization and journal founded by the leaders of the 1968 Mexican student movement, and later Convergencia Comunista 7 de enero (CC7). He became an important student leader and representative to UNAM's University Council and gained national prominence with the creation of the in 1986.