On 27 June 1956, he was appointed Titular Bishop of Messene by Pope Pius XII. Angelini received his episcopal consecration on 29 July from Cardinal Giuseppe Pizzardo, with Archbishop Luigi Traglia and Bishop Ismaele Castellano serving as co-consecrators. He founded, in 1959, the Italian Catholic Doctors' Association, and attended the Second Vatican Council (1962–1965). On 6 January 1977, Pope Paul VI named him an Auxiliary Bishop of Rome. Pope John Paul II raised him to the rank of Archbishop and appointed him as the first president of the newly created Pontifical Council for the Pastoral Care of Health Care Workers on 16 February 1985. He was created Cardinal-Deacon of "Santo Spirito in Sassia" by John Paul II in the consistory of 28 June 1991.