Arco was born on the estate of his father, Count Alexander Karl von Arco, in Großgorschütz, Upper Silesia, Prussia (now Gorzyce, Poland). He belonged to the Arco family, of Italian origin. His noble title was abolished when Germany became a republic after the First World War. As a child he was interested in machines of all kinds, but after graduating from the Maria Magdalenen High School in Breslau (now Wrocław, Poland) in 1889, he did not study engineering sciences, but instead attended mathematical and physical lectures at the University of Berlin. Afterwards he took up a military career, a family tradition. After three years with the military, however, he left to study mechanical engineering and electro-technology in the technical university in Charlottenburg, Berlin, from 1893. There he became acquainted with Professor Adolf Slaby, who had participated in Guglielmo Marconi's transmission experiments on the coast of the English Channel.