O'Rourke was born October 26, 1876 in Basin, Minsk, Russian Empire (modern Belarus), to an aristocratic family of Irish ancestry, many of them high officers in the Russian military. They held imperial titles of the Russian Empire and of the German Holy Roman Empire, but also had petitioned to retain the Irish count title as well, which was granted by the Tsar in 1848. His father was Michael Graf O'Rourke and his mother Baltic-German Angelika von Bochwitz. He received a widespread European education and learned a number of languages. After graduating from the famous Jesuit college in Chyrów (then Russia, now Ukraine), in 1898 he went to Riga, Latvia, where in 1903 he graduated from the Trade and Mechanics Faculty of the University of Riga. In 1903 he moved to Freiburg, Switzerland, where he continued his studies at the faculty of law, but the following year he moved to the theological faculty at the University of Innsbruck in Austria-Hungary.
On October 27, 1908 he was ordained a priest in Vilna (Vilnius, Lithuania), and in 1918 he became the bishop of Riga.
Having hosted synode on 10 to 12 December 1935, growing pressure from the Nazi majority senate made him resign as bishop of Danzig. On 13 June 1938 he was appointed Titular bishop of Sophene ernannt. He adopted Polish citizenship in the same year as well as the office of Domkapitular in Gnesen/Posen. When after September 1939 most Polish bishops fled Poland, the Germans considered him as diocese administrator for western Poland, but O'Rourke soon moved to Rome, where he died on June 27, 1943.
His successor after his death was the bishop of Danzig Carl Maria Splett.
In 1972 his ashes were moved from Campo Verano to his former bishopric to be buried in a crypt in the Oliwa Cathedral.