At the regular election held in any State next preceding the expiration of the term for which any Senator was elected to represent such State in Congress, at which election a Representative to Congress is regularly by law to be chosen, a United States Senator from said State shall be elected by the people thereof for the term commencing on the 3d day of January next thereafter.
2 U.S. Code § 1 - Time for election of Senators
1934—Act June 5, 1934, substituted “3d day of January” for “fourth day of March”.
The first section of Amendment XX to the Constitution provides in part: “* * * the terms of Senators and Representatives [shall end] at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.”
Time for election of Senators, see Const. Art. I, § 4, cl. 1.
Vacancies in the Senate, see Const. Amend. XVII.