Adelita Grijalva has not been sworn in as a member of Congress, due to the government being shut down. Does it have to be Congress that swears her in? Could she be sworn in by a federal judge?
Yes.
So ‘Yes, they can be sworn in by a federal judge, but only after they have taken official oaths in Congress’?
Yes but that is because of a (probably unconstitutional) act of congress. They have added a requirement to being a congressman that wasn’t in the constitution.
2 USC 25
At the first session of Congress after every general election of Representatives, the oath of office shall be administered by any Member of the House of Representatives to the Speaker; and by the Speaker to all the Members and Delegates present, and to the Clerk, previous to entering on any other business; and to the Members and Delegates who afterward appear, previous to their taking their seats.
So it has to be the Speaker doing the swearing in (according to the law as it exists).
Just to answer the inevitable “Who swears in the Speaker?” The Speaker is chosen by vote of the House members who won election the previous November (with some conceivable exceptions for special elections that I can’t remember happening). As said in 2 USC 25, any member can do so, probably since they are all equal nullities at this moment. Then the Speaker swears in all the other members.
Some interesting and odd tidbits are available online.
[House Practice: A Guide to the Rules, Precedents and Procedures of the House]
[Chapter 33. Oaths]
That the Speaker swears the members in en masse didn’t start until the 71st Congress.
And provision is made for an absent Speaker.
Sec. 2 . Absent Members and the Oath; Use of Deputies
The Speaker, or a deputy named by him, may be authorized by resolution to administer the oath of office to a Member-elect absent because of his illness or because of some illness in his family. Deschler Ch 2 Sec. Sec. 5.8-5.12. The resolution may authorize the administration of the oath at some location other than the House. 1 Hinds Sec. 170; 6 Cannon Sec. 14. Persons who may be designated by the Speaker to administer the oath to an absent Member-elect include another Member (Deschler Ch 2 Sec. 5.10), a State or county judge (Deschler Ch 2 Sec. 5.11), or a Federal district court judge (105-1, Feb.
None of that is applicable here, unfortunately.