Born in New Haven, Connecticut, to Rachel Andrews and Myer Moses, an immigrant from England, Isaac grew up with his six siblings in Charleston. In 1802, he married Hannah Lazarus, daughter of Mark and Richa Benjamin Lazarus, and they raised their twelve children in Charleston. Listed in Charleston directory as a justice of the peace in 1819, the following year Isaac founded a law firm with Christian Stanley. He helped found the Reformed Society of Israelites together with dramatist and editor Isaac Harby, whose daughter Octavia married Isaac’s son, Andrew. Isaac’s daughter Cecilia married the painter Theodore Sydney Moise, who painted portraits of Isabel Mordecai and Isaac’s granddaughter Caroline Lopez. While in Branford, Connecticut, Isaac and Hannah were thrown from a buggy, and Isaac died, making him the first known Jew to be buried in Connecticut, while Hannah died the following year from her injuries.