According to the Wikipedia:
“Ma’oz Tzur” is thought to have been written in the 13th century, during the Crusades.[1] The first letters of the first five stanzas form an acrostic of the composer’s name, Mordechai (the five Hebrew letters מרדכי). He may have been the Mordecai ben Isaac ha-Levi who wrote the Sabbath table-hymn “Mah Yafit”,[2] or even the scholar referred to in the Tosafoth to Talmud (Bavli) Niddah 36a. Or, to judge from the appeal in the closing verse, he may have been the Mordecai whose father-in-law was martyred at Mayence (now Mainz, Germany) in 1096.