Two Oaths for Justices
At SCOTUSBlog, Mark Walsh describes the swearing-in of Justice Gorsuch:
Gorsuch must take two oaths for the position of associate justice, the “constitutional oath” administered to all federal officials under Article VI of the Constitution and the “judicial oath” required under the Judiciary Act of 1789.
How and where these oaths have been administered to new justices, and even how many times, has varied widely in recent years. Six of the eight current members of the court participated in White House events at which they took the constitutional oath, even if that was purely for ceremonial reasons.
All eight, as most of their predecessors had, separately participated in the court’s investiture ceremony, which I’ll describe in further detail below, in which they took the judicial oath (again, sometimes just for ceremony) before taking their seats on the Supreme Court bench for the first time. For various reasons, most current justices first took one or both of their oaths privately.
5 U.S. Code § 3331 - Oath of office
An individual, except the President, elected or appointed to an office of honor or profit in the civil service or uniformed services, shall take the following oath: “I, AB, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.” This section does not affect other oaths required by law. (Pub. L. 89–554, Sept. 6, 1966, 80 Stat. 424.)
28 U.S. Code § 453 - Oaths of justices and judges
Each justice or judge of the United States shall take the following oath or affirmation before performing the duties of his office: “I, ___ ___, do solemnly swear (or affirm) that I will administer justice without respect to persons, and do equal right to the poor and to the rich, and that I will faithfully and impartially discharge and perform all the duties incumbent upon me as ___ under the Constitution and laws of the United States. So help me God.” (June 25, 1948, ch. 646, 62 Stat. 907; Pub. L. 101–650, title IV, § 404, Dec. 1, 1990, 104 Stat. 5124.)