Buuxi weedha soo socota: Yooxanaa XXIII wuxuu ku magacaabay Cardinal-Deacon of "Sant'Eugenio" ee Consistory-ka 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 qeyb galay Golaha Labaad ee Vatican 1962 ilaa 1965, wuxuuna ka qeyb qaatay
1963 shirkii lagu doortay Pope Paul VI.