2 U.S. Code § 23 - Presiding officer of Senate may administer oaths
The presiding officer, for the time being, of the Senate of the United States, shall have power to administer all oaths and affirmations that are or may be required by the Constitution, or by law, to be taken by any Senator, officer of the Senate, witness, or other person, in respect to any matter within the jurisdiction of the Senate.
Source(Apr. 18, 1876, ch. 66, § 1,19 Stat. 34.)