Eskenazi was born Sarah Skinazi to an impoverished Sephardic Jewish family in Istanbul. Throughout her career she hid her real date of birth, and claimed to have been born in 1910. In fact, she was at least a decade older, and was likely born sometime between 1895 and 1897. Her father, Avram Skinazi, was a rag dealer. In addition to Roza, he and his wife Flora had two sons, Nisim, the eldest, and Sami.