There are two oaths of office administered. The constitutional oath and the judicial oath. Traditionally the Chief Justice administers the constitutional oath. I believe that the Chief Justice also typically administers the judicial oath (although Kennedy administered it to Gorsuch who had been his law clerk).
After the Senate confirms a judge, the President must issue a “commission” which he signs and then is countersigned by the Attorney General. See here. The commission is then presented to and accepted by the Court. (Although, I don’t think it can be rejected, the judge becomes a judge when the commission is signed). And then the judge can be sworn in.
I don’t know what timeframe is standard. But Gorsuch was confirmed on April 7. His commission was dated April 8 and he was sworn in on April 10. So, he could probably be on the bench by Tuesday.
ETA: Kagan was confirmed on August 5 and sworn in on August 7.
Gorsuch was sworn in on Monday, April 10th after the confirmation vote on Friday the 7th. He had a private ceremony with the oath administered by the Chief Justice that met the requirements. It was followed by a public swearing in by Trump in the Rose Garden; Kennedy administered the additional oath that justices take at that ceremony. (Cite)
There is an interim step between the vote and oath. The President has to formally apoint the Justice after the Senate has consented. (Cite) That cite also looks at how the separate oaths took hold and changing traditions. Early on, many Justices were sworn in by someone in their home state after appointment since they started their duties with the regional circuit courts before heading to DC. The first oath ceremony at the White House wasn’t until 1940 and there’ve been some changes in traditions since then.
I’d never given any thought to how Justices are sworn in after the Senate confirmation.
It’s about time that I learned.
Supreme Court vacancies usually doesn’t happen very often. The court’s had several justices retire and one die. So we’re getting more replacements than usual.
An interesting case in this regard is that of Clarence Thomas. He was confirmed on October 15, 1991, but it appeared as if his swearing in would be delayed because the wife of Chief Justice Rehnquist died on October 17. Thomas requested the delay to be reduced so he could take up office as soon as possible, and he was sworn in on October 19.