The Constitution does not give any details about the Oath of Office to be taken by Justices of the Supreme Court.
Article 6 covers oath:
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
But we find in United States Code (Title 28, Chapter I, Part 453) the oath Justice of the SCOTUS:
"I, [NAME], 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 [TITLE] under the Constitution and laws of the United States. So help me God."
"Without respect to persons…."