After receiving minor orders at Reims in 1590, Norris went to the Venerable English College, Rome, where he completed his studies and was ordained priest.
In May, 1596, he was sent on the English mission, and was one of the appellant clergy in 1600. In the prosecutions following upon the Gunpowder Plot, Norris was committed to the Bridewell. From his prison he addressed a letter to the Earl of Salisbury, dated 1 December 1605, in which he protests his innocence, and in proof of his loyalty promises to repair to Rome, and labor so that the pope shall bind all the Catholics of England to be just, true, and loyal subjects, and that hostages shall be sent "for the afferminge of those things".