Hacham Raphael Yitzhak Israel, son of Hacham David, was born in Rhodes, in 1809, while it was under Ottoman rule. He married Reina, the daughter of Hacham Michael Yaakov Israel, who was Chief Rabbi of Rhodes. In 1840, his father-in-law was among those interrogated about the death of a Christian youth during a blood libel. He was hung on an iron hook by European consuls for two days but refused to confess to the false accusation. Hacham Raphael Yitzhak married a second wife, whose father, Hacham Yaakov Entebbe, was the Rabbi of Damascus. The latter was accused of the murder of a Christian priest in the 1840 blood libel in Damascus and cruelly tortured for six months.
In 1853 Hacham Michael Yaakov Israel immigrated to the Land of Israel and Hacham Raphael Yitzhak Israel was appointed to replace him as Chief Rabbi of Rhodes. Hacham Raphael Yitzhak Israel labored diligently on community legislation and was strict about having the market's shops close in time to ensure that the public would participate in the 'Arvit evening prayer. After an earthquake occurred on the island, he left for Europe to raise money.
In 1861 he published Hacham Haim Shlomo Tarsa's Haim Shanim in Izmir. He immigrated to the Land of Israel in 1881, where he was appointed President of the Sephardi community's Rabbinic Court. The members of his court were Hacham Nissim Burla and Hacham Yaakov Matalon, as well as Hacham Abraham (the son of Hacham Shlomo Mevorach) and Hacham Yechiel Bar Adon.
His book of sermons, Beit HaYayin, was published in Izmir in 1883, and in 1900 Kol Koreh was published in Jerusalem. His halakhic rulings and articles are quoted in many books, including Pitchei Teshuva by Hacham Hizkiyah Shem Tov, Mateh Lekhem by Hacham Raphael Haim Franji, in books by Hacham Haim Faladji and by his son, Hacham Abraham Faladji, in Kevod Yaakov, Shaarei Rahamim, and VaYeshev Yoseph. His articles were published in religious journals, including Torah Me'Tzion and HaMe'aseph.
Hacham Raphael Yitzhak Israel passed away on 7 Tammuz, 5652 (1902).