Orr was born in Kfar Haim in 1939. He was drafted into the Israel Defense Forces in 1957, serving with the Armored Corps. During the Six-Day War he commanded 7th Brigade, which advanced through the northern shore of the Sinai Peninsula. In the War of Attrition he commanded an armored battalion in the Sinai and the Jordan Valley. He was made Lieutenant Colonel in August 1973, becoming the commander of the newly formed 679 (reserve) Brigade, which he led during the Yom Kippur War.
Following the Yom Kippur War, Orr was assigned to command 7th Brigade. In 1976 he was made commander of an armored division on the Golan Heights, with the rank of Brigadier General, and later served as Chief of Staff of Central Command. In 1981 he was advanced to the rank of General, heading Central Command between 1981 and 1983 and Northern Command between 1983 and 1987, partly during the First Lebanon War.
Orr is the author of two biographical books: "Follow Me"  (Hebrew: אחרי), and "These are My Brothers"  (Hebrew: אלה האחים שלי).