Aruj or Arouj (Turkish: Oruç Reis, Arabic: عروج بربروس, Spanish: Arrudye; c. 1474 – 1518) was the elder brother of Barbarossa Hayreddin Pasha and Ottoman Bey (Governor) of Algiers and Beylerbey (Chief Governor) of the West Mediterranean. He was born on the Ottoman island of Midilli (Lesbos in today's Greece) and was killed in a battle with the Spaniards at Tlemcen in the Ottoman Eyalet of Algeria.

He became known as Baba Aruj or Baba Oruç (Father Aruj) when he transported large numbers of Moriscos refugees from Spain to North Africa; he was known through folk etymology in Europe as Barbarossa (which meant Redbeard in Italian).

Sources refer to him as a Greek, as a Turk or as an Albanian by origin. Oruç was born in the 1470s on the Ottoman island of Midilli (Lesbos in present-day Greece; Greek: Λέσβος) to his father Yakup Ağa, a Greek renegade or Turk as well as a former Sipahi from the Ottoman city of Yenice-i Vardar (modern Yannitsa in Greece) and his wife, Katerina, from the Aegean island of Lesbos. Yakup Ağa took part in the Ottoman conquest of Lesbos (Midilli) from the Genoese in 1462, and as a reward, was granted the fief of the Bonova village in the island. He married a local Christian Greek woman from Mytilene, the widow of an Orthodox priest, named Katerina, and they had two daughters and four sons: Ishak, Oruç, Hızır and Ilyas. Yakup became an established potter and purchased a boat to trade his products. The four sons helped their father with his business, but not much is known about the daughters. At first Aruj (Oruç) helped with the boat, while Hızır helped with pottery.