Yes they did. Armata Italiana in Russia or the Italian Army in Russia. Known as the Eight Italian Army. Fought in Russia from July '42. This replaced or more accurately augmented the Italian Corps in Russia. Which had been fighting since August '41, or since just after Barbarrosa.

The Italian fought in the South, basically the Ukraine and the Caucasus. They were on the flank of the German Sixth Army. And were badly mauled at Stalingrad. After the surrender of Von Paulus and his men, in early to mid, '43 they were brought back to Italy.

The Italians had some notable success in fighting, on the Don river, but generally suffered regular reversals, and were considered poorly trained and equipped.

Sources: Jowett, Philip S. The Italian Army 1940–45 Paoletti, Ciro (2008). A Military History of Italy