From the Catholic Encyclopedia:
The date of its composition has long been a disputed question. Many critics whose names must be mentioned with respect, among them Dozy and Ticknor, place it at the beginning of the thirteenth century; but today the best opinion places the poem a half-century earlier. Among those who think it was written as early as the middle of twelfth century are many eminent Spanish and foreign scholars, including Sanchez, the first editor of the poem, Capmany, Quintana, Gil y Zarate, Bouterwek, Sismondi, Shlegel, Huber, and Wolf. The learned Amador de los Rios, whose opinion carries great weight, thinks that the famous poem must have been written prior to 1157.