On 5 November 1985, Pope John Paul II appointed Rivera Bishop of Tehuacán. Archbishop Antonio López Aviña consecrated him bishop on 21 December with Archbishops Adolfo Suárez Rivera and Rosendo Huesca Pacheco as co-consecrators. He headed the Mexican Episcopal Conference's Commission for the Family from 1989 to 1995 and the Family Section of the Latin American Episcopal Conference from 1993 to 1995. Rivera was named Archbishop of Mexico City on 13 June 1995, which made him ex officioPrimate of Mexico. John Paul II made him Cardinal-Priest of S. Francesco d'Assisi a Ripa Grande in the consistory of 21 February 1998. In 2001, he called charges of sexual abuse on the part of Marcial Maciel Degollado, the leader of the Legion of Christ, "a plot." In 2002, Rivera criticized the US media for its coverage of clergy sexual abuse. He called it "an orchestrated plan for striking at the prestige of the Church." He compared it to "what happened in the past century with the persecutions in Mexico, in Spain, in Nazi Germany and in communist countries." Rivera was one of the cardinal electors who participated in the 2005 papal conclave that elected Pope Benedict XVI. He was mentioned as a possible choice for pope at the time, as he had been years earlier. Within the Latin American Episcopal Conference, Rivera served as President of the Episcopal Committee of Culture from 2004 to 2006. He is also a member of the Pontifical Council for the Family, the Congregation for the Clergy, and the Congregation for Divine Worship and the Discipline of the Sacraments. He was made a member of the Congregation for Institutes of Consecrated Life in 2014. He is seen as a strong advocate of social justice: his criticism of globalization and political corruption so annoyed Mexico's Salinas government that it threatened to adopt a law forbidding priests from commenting on politics. Rivera Carrera is a conservative on virtually all church matters. In 1990, as Bishop of Tehuacán, he closed a seminary that he said was teaching Marxist theology. In 1996, he forced the resignation of the abbot of the basilica of Our Lady of Guadalupe after he had questioned the historical truth of Mary's appearance to Juan Diego. He denounced the legalization of same-sex marriage and adoption by same-sex couples in 2009 and 2010. He said: "Our children and youth run the grave risk of seeing these types of unions as normal and they can falsely understand that sexual differences are simply a personality type.... Homosexual acts, in effect, close the sexual act to the gift of life. They do not come from a true affective and sexual complementarity." In 2011, as the Supreme Court of Mexico prepared to deliberate on a ruling proposed by Justice Fernando Franco that would overturn anti-abortion constitutional amendments enacted in numerous Mexican states. Rivera Carrera said that "abortion is never a solution for anything." On 25 September he said: "The Church always reaches out to pregnant women who are being pressured at work, by family members or friends to remind each one of them of the great value of motherhood." He noted that the Mexican bishops emphasized that the "taking of human life through the various abortifacient techniques must not be tolerated, and the taking of the life a human being, even in its initial phases, is not licit." He was one of the cardinal electors who participated in the 2013 papal conclave that elected Pope Francis. On 13 February 2016, Francis addressed the bishops of Mexico and appeared to castigate them: "Do not lose time or energy in secondary things, in gossip or intrigue, in conceited schemes of careerism, in empty plans for superiority, in unproductive groups that seek benefits or common interests. Do not allow yourselves to be dragged into gossip and slander." In March, an editorial in the newspaper of the Mexico City Archdiocese defended the bishops and said that the pope had received "bad advice." Observers identified Rivera as both a target of the Pope's speech and the source of the editorial response.
Sexual abuse case
Beginning in 1989, Los Angeles prosecutors pursued a Mexican priest on charges of sexual abuse while he was stationed in the US for more than a decade. A lawsuit filed there charged that as Bishop of Tehuacán and Los Angeles Cardinal, Roger Mahony had shielded a priest abuser. Rivera said that when he approved the priest's transfer to Los Angeles, he had heard "accusations of homosexuality, but not of pedophilia." Rivera asked the Vatican to defrock the priest in 2007.