No, the Bible nowhere mentions an angel named Raphael. Only two holy angels are named in Scripture—Gabriel (Luke 1:26) and Michael (Daniel 12:1), the latter designated as an “archangel” in Jude 9. The angel Raphael does appear in the apocryphal book of Tobit (or Tobias), which is considered inspired by the Catholic Church. In that account, Raphael disguises himself as a human, keeps the younger Tobias safe on a journey, chases away a demon, and heals the elder Tobias of his blindness. Because of these actions, Raphael is considered by Catholics as the patron of the blind, of travelers, and of physicians.
In the book of Tobias, Raphael identifies himself as one of seven archangels “who stand before the Lord” (Tobit 12:15). Raphael also offers prayers on Tobias’ behalf, and Tobias, in turn, thanks the angel because he is “filled with all good things through him” (Tobit 12:3).
John sheds some light on the religious notions in the time of Christ. “A great multitude of sick people” are sitting beside a pool in Jerusalem, waiting for “the moving of the water.” They believed that an angel would descend from heaven and stir the water, making the pool a place of healing for them. Jesus approaches a man who had been infirm for 38 years and asks him if he wants to be healed. The man’s sad, superstitious reply is that he cannot be healed, because he cannot get into the pool quickly enough. Jesus then bypasses all superstition and shows His power to immediately heal the man (John 5:3-9).
Although the Book of Tobias was not included in the Hebrew Scriptures, the Septuagint did include it; therefore, the story of Raphael would have been familiar to almost everyone in Jesus’ day. It is quite possible that the “angel of the pool” the sick man was waiting for was, in his mind, Raphael. It is interesting that Raphael never shows up in John 5. It is Jesus, not an angel, who “heals all your diseases” (Psalm 103:3).