He was consecrated a bishop without papal mandate, on July 28, 1991 at São Fidelis in Rio de Janeiro, Brazil, Bernard Tissier de Mallerais, assisted by Alfonso de Galarreta and Richard Williamson (all three from Society of St. Pius X).
He succeeded bishop Antônio de Castro Mayer in 1991 as superior of the Priestly Society of Saint John Mary Vianney, an association of priests in the diocese of Campos, Brazil.
On August 15, 2001, Bishop Rangel, together with 25 priests, reconciled with the Holy See. He addressed a letter to the Pope John Paul II in which he expressed an act confirming full submission to and communion with Rome. The Pope created the Personal Apostolic Administration of Saint John Mary Vianney, and appointed him the apostolic administrator for the pastoral care of the faithful who remain attached to the Tridentine Liturgy. He held the title of Titular Bishop of Zarna from 2002 until his death.
Because of his health, he asked for an auxiliary bishop. The Pope instead instructed Bishop Rangel to ask for a coadjutor bishop. Fernando Rifan was chosen to be this new coadjutor, and after after Bishop Rangel's 2002 death, he was then automatically succeeded by Bishop Rifan.