Ku sii wad qodobkan - John XXIII wuxuu ka dhigay Cardinal-Deacon of "Sant'Eugenio" ee kulanka 28-kii Maarso 1960. Kadinal Bacci waxaa markii dambe loo magacaabay inuu yahay hoggaamiyaha kiniisadda "Colonia ee Cappadocia" 5tii Abriil 1962, wuxuuna helay quduusnimadiisa kiniisadeed 19-kii Abriil ee soo socota John XXIII, iyadoo Cardinals Giuseppe Pizzardo iyo Benedetto Aloisi Masella ay u adeegayaan sidii co-consecrators. Wuxuu ka qaybgalay Golaha Labaad ee Vatican 1962 ilaa 1965, wuxuuna ka qaybgalay shirkii 1963 ee ka dhacay Vatican
kaas oo doortay Pope Paul VI.