On 13 February 1960, Bafile was appointed Apostolic Nuncio to Germany and Titular Archbishop of Antiochia in Pisidia on 13 February 1960 by Pope John XXIII. He received his episcopal consecration on the following 19 March from John XXIII himself, with Archbishop Diego Venini and Bishop Petrus Canisius Van Lierde, OSA, serving as co-consecrators, at the Sistine Chapel. He attended the Second Vatican Council from 1962 to 1965, and was later named Pro-Prefect of the Congregation for the Causes of the Saints on 18 July 1975.