Angelini received his episcopal consecration on 29 July from Cardinal Giuseppe Pizzardo, with Archbishop Luigi Traglia and Bishop Ismaele Castellano serving as co-consecrators.

Due to his responsibility for the health of the Vatican (head of the Pontifical Council for the Pastoral Care of Health Care Workers, 1985–1996), which made him the leader of 3,000 institutions in Italy alone, Angelini (nicknamed Sua Sanità) was involved in the Tangentopoli bribery scandal of the early 1990s.

[1] Accusations against him included the forced acceptance of his own people for public commissions, as well as extortion from a pharmaceutical company.

Angelini celebrated the marriage of the daughter of Paolo Cirino Pomicino, another DC politician involved in the bribery scandals; the marriage was attended, amongst others, by Andreotti, Gianni De Michelis (also put on trial in the Tangentopoli scandal) and minister Francesco De Lorenzo, who was condemned to 5 years imprisonment for bribery in the management of Italy's Public Health sector.

In a 1992 sermon in Saint Peter Basilica on the anniversary of the death of the pontiff, Angelini stated that his career had suffered because of his positive views of Pope Pius XII.