When a President of the Senate has not taken the oath of office, it shall be administered to him by any Member of the Senate.
Structure US Code
CHAPTER 2— ORGANIZATION OF CONGRESS
§ 22. Oath of President of Senate
§ 23. Presiding officer of Senate may administer oaths
§ 24. Secretary of Senate or assistant secretary may administer oaths
§ 25. Oath of Speaker, Members, and Delegates
§ 25a. Delegate to House of Representatives from District of Columbia
§ 26. Roll of Representatives-elect
§ 27. Change of place of meeting
§ 28. Parliamentary precedents of House of Representatives
§ 28c. Distribution of Precedents by Director of the Government Publishing Office
§ 29a. Early organization of House of Representatives
§ 30a. Jury duty exemption of elected officials of legislative branch