Rodziński was the son of a General of Polish-Jewish origin in the Austro-Hungarian army. His father was stationed in Split on the Dalmatian coast, then capital of the Austrian Crown land of Dalmatia. Shortly after the birth of Artur family moved to Lembergnow Lviv. Artur spent most of his youth here by. After high school he studied music in Lemberg, after which he began to study law in Vienna . However, he enrolled at the Conservatory, where he studied conducting with Franz Schalk . Franz Schreker and his teachers were Josef Marx composition and Emil von Sauer and Jerzy Lalewicz his piano teachers. Back in Lemberg, he was conductor of the opera chorus and in 1920 he made his debut as a conductor with Verdi's Ernani . In Warsaw he conducted the Philharmonic Orchestra of Warsaw and the Polish national opera. During a visit to Poland Rodziński's Leopold Stokowski visited one of concerts, in which he invited the young conductor for a guest conducting with his Philadelphia Orchestra. Rodziński accepted and worked from 1925 to 1929 as Stokowski's Assistant in Philadelphia. He led here both symphonic concerts and opera performances. In 1929, he was appointed Chief conductor of the Los Angeles Philharmonic Orchestra and in 1933 he exchanged that function for the same position at the Cleveland Orchestra, where he succeeded Nikolai Solokoff . He wore an important role at that this Orchestra the "most European" of the American orchestras was.
Rodziński's choice of repertoire was original and taste makers. So he spent with his Orchestra the first American performance of the opera Lady Macbeth of the Mtsensk district by Dmitri Shostakovich in 1942 and he was one of the first to his seventh Symphony conducted. With the Orchestra he also made numerous recordings. His American fame brought him back in Europe, where he in 1936 and 1937 conducted the Vienna Philharmonic Orchestra at the Salzburg Festival. Between 1934 and 1937 he was also principal guest conductor of the New York Philharmonic. This Orchestra appointed him in 1943 to chef. He would stay there four years, a period which resulted in high-quality music, but otherwise marked by many conflicts with the Orchestra directors. He was not long without Orchestra. The Chicago Symphony Orchestra in the same year appointed him Chief, but also here made his inflexible character the cooperation with the Board so tricky, that he left after just one season. In that one season, he led a number of historic performances of Wagner'sTristan und Isolde with the Norwegian soprano Kirsten Flagstad in one of the title roles. Rodziński returned to Europe. Because his health to be desired left no more permanent jobs, he accepted, but he was seen there as a guest conductor and led numerous recordings. So he gave the first performance of the opera war and peace by Prokofiev and he led in the Scala Tristan and Isolde and in that time carried out in Italy little operas of Modest Mussorgsky: Boris Godunov and Khovantsjina.
Although his health was getting worse and an Italian doctor tried to move him to work less, he returned to Chicago, where he in 1958 a series of performances of Tristan und Isolde was leading the Swedish sopranoBirgit Nilsson in the title role. Although the opera was a success, the effort was too much for the conductor. He died a short time later in Boston. Rodziński left his (second) wife, Halina, and a son Richard behind. His first wife Sarah, with whom he was married from 1917 to 1934, was a concert pianist. Halina Rodzinski published the autobiography in 1976 Our two lives, which as a major source for the life of her husband applies.