Darline Graham, the younger sister of Senator Lindsey Graham, was sworn in on Tuesday as his interim replacement, taking the South Carolina Republican’s seat just three days after his sudden and unexpected death.

Standing in the Old Senate Chamber, Ms. Graham placed her hand on a Bible held by her husband, Larry Nordone, and vowed to serve out the remainder of her brother’s term, which ends in January.

The chamber was filled with long sighs and teary eyes as Senator Charles E. Grassley, Republican of Iowa and the president pro tempore of the chamber, administered the oath.

Ms. Graham was tapped on Monday by Gov. Henry McMaster of South Carolina to fill Mr. Graham’s seat after he died Saturday night from what a preliminary medical report said was a tear in his aorta. His death, at 71, left his Republican colleagues in the Senate bereaved and facing fresh challenges in moving an agenda that already faced substantial hurdles.

Ms. Graham, 62, has no direct experience in Washington politics aside from supporting her brother, and has never been elected to serve public office. A mother of two and a lifelong South Carolinian, she has spent her career primarily in state government — first with the state’s employment and vocational departments and more recently as leader of the South Carolina Commission for the Blind.

Mr. Graham’s death came as he was favored to win re-election for a fifth term in November. Republicans are already planning a special primary to replace Mr. Graham on the ballot, though Ms. Graham has indicated she would not run in that contest.

There is a long history in American politics of having the widowed wives of men who die in office finish out their terms. Ms. Graham’s appointment is a fresh spin on the tradition.

Mr. Graham never married, and often described his sister as his closest family. The two developed a deep bond while growing up in the back room of a bar in Central, S.C., and Mr. Graham even became Ms. Graham’s legal guardian after the deaths of their parents. In his long-shot run for president in 2015, Mr. Graham suggested that Ms. Graham could be his first lady.

Ms. Graham was flanked on Tuesday by Senators Tim Scott of South Carolina and Katie Britt of Alabama, both Republicans.

Other members of South Carolina’s congressional delegation also attended, including some of the members who may vie for the seat Ms. Graham is currently holding: Representatives William R. Timmons IV, Ralph Norman and Joe Wilson. Treasury Secretary Scott Bessent, also rumored to be considering a run, was in attendance.

In a congratulatory post on social media, Representative James E. Clyburn, the long-serving Democrat from South Carolina, noted that Ms. Graham’s swearing-in amounted to two milestones for the state: She is the first woman and the first graduate of a historically Black university — South Carolina State University — to represent South Carolina in the Senate.

It is unclear what committees Ms. Graham will be assigned to join. Her brother was chairman of the Budget Committee and served on the Judiciary, Appropriations and Environment and Public Works Committees. But it would take a unanimous agreement among all senators to allow Republicans to fill the vacancies left by Mr. Graham’s death.

Catie Edmondson contributed reporting.