Upon leaving BYU, Oaks was appointed as a justice of the Utah Supreme Court on January 1, 1981, by Utah governor Scott M. Matheson. He served in this capacity from 1980 to 1984, when he resigned after being appointed by the LDS Church as a member of the Quorum of the Twelve Apostles. In 1975, Oaks was listed by U.S. attorney general Edward H. Levi among potential Gerald Ford Supreme Court candidates. In 1981, he was closely considered by the Ronald Reagan administration as a Supreme Court nominee.