General Discussion

Yes, there is historical precedent for a judge swearing in a member of Congress, WHEN AUTHORIZED BY A RESOLUTION PASSED BY THE HOUSE

So, absent such a resolution being adopted -- and I'm willing place a sizable wager this Repub majority Congress isn't going to do that -- no judge will be authorized to swear Grijalva.

To further substantiate my post, here is a link to the official "Precedents of the U.S. House of Representatives." https://www.govinfo.gov/content/pkg/GPO-HPREC-PRECEDENTS-V1/pdf/GPO-HPREC-PRECEDENTS-V1.pdf

The rules and precedents governing the swearing in of members are found in Chapter 2, and the specific rules and precedents governing the deputization of someone other than the Speaker to administer the oath are found in Section 3.1 of Chapter 2. I direct attention to the bottom of page 182, wherein it is stated:

"The House may also authorize the Speaker to deputize another to administer the oath of office. Most often, this is done when the Member–elect cannot travel to Washington, D.C., to be present on opening day of a new Congress (due to illness, for example). For these circumstances, the House will adopt a resolution conferring on the Speaker the authority to name a deputy to administer the oath.(23) Such resolutions are privileged for consideration.(24) The Speaker may deputize anyone to administer the oath of office, though this function is typically performed by a Federal or state judge,(25) and occasionally by another Member of the House.(26) When the oath is administered, the person deputized to administer the oath informs the Speaker, who lays such communication before the House.(27) The House formally ‘‘accepts’’ the oath administered by a deputy, either in the resolution authorizing the Speaker to deputize(28) or by separate resolution.(29)
23. See § 3.13, infra. See also Deschler’s Precedents Ch. 2 §§ 5.8–5.12.
24. See, e.g., H. Res. 8, 133 CONG. REC. 19, 100th Cong. 1st Sess. (Jan. 6, 1987) and H.
Res. 25, 133 CONG. REC. 820, 821, 100th Cong. 1st Sess. (Jan. 7, 1987)
25. See § 3.13, infra.
26. See 129 CONG. REC. 52, 98th Cong. 1st Sess. (Jan. 3, 1983). 27. See § 3.14, infra.
28. See § 3.13, infra.
29. See § 3.15, infra.

Examples of such resolutions can be found at pages 199-202.