After the death of Andrea, Francesco was appointed professor of civil law at the university of Pavia.

Alciati was a close friend of Gerolamo Cardano and advocated his candidacy to the chair of the theory of medicine at Bologna in 1562.

[2] Cardano at once named AIciato as his personal representative in Bologna, with the power to arrange the details of salary.

Called to Rome by Pius IV, he was appointed apostolic referendary, and nuncio to the king of Bohemia; he was then appointed bishop, datary, pro-camerlengo, Cardinal deacon of Santa Maria in Campitelli and Cardinal priest of Santa Susanna.

He died in office and was buried in Rome in the Carthusian Church of Santa Maria degli Angeli.