John XXIII created him Cardinal-Deacon of "Sant'Eugenio" in the consistory of 28 March 1960. Cardinal Bacci was later named titular archbishop of "Colonia in Cappadocia" on 5 April 1962, and received his episcopal consecration on the following 19 April from John XXIII, with Cardinals Giuseppe Pizzardo and Benedetto Aloisi Masella serving as co-consecrators. He attended the Second Vatican Council from 1962 to 1965, and participated in the 1963 papal conclave that elected Pope Paul VI.