Trump wrote on Truth Social.
Nordone, who has never held public office, previously served as the commissioner of the South Carolina Commission for the Blind since 2019 and held prior roles at Clemson University.
"I promise to work hard over the next several months to support the president and carry forward the efforts of my brother on behalf of the citizens of South Carolina and the United States," said Nordone.
She expressed her belief that taking on this legislative role was the most appropriate way to pay tribute to her brother's memory.
"I think this is what Lindsey would have wanted, and I plan to honor him in this way," she remarked.
During his 2016 presidential campaign, Lindsey Graham had humorously suggested his sister could step into a prominent public role if he ever reached the White House.
"Well, I've got a sister. She could play that role if necessary," he joked when asked about a first lady.
Years earlier, Graham had also spoken highly of his sister's potential to represent the nation on a broader stage.
"She would be a great representative of our country.
I can't think of a better person to represent our country in an event than my sister," Graham said in 2015.
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At the time of his death, Graham was seeking a fifth Senate term after winning the Republican nomination last month, with a special Republican primary now scheduled for next month to determine the permanent nominee for the November ballot.
