Yes.

South Dakota’s electoral votes have gone to a non-Republican candidate for president five times, but the last time was more than 60 years ago.
Lyndon Johnson was the last Democratic candidate to win the state’s electoral votes, winning 55.6% of the vote against Republican Barry Goldwater in 1964.
Before that, the state's electoral votes went to Democrat Franklin D. Roosevelt for his first and second terms in 1932 and 1936. In 1912, the state was one of six that voted for Theodore Roosevelt, who ran in the Progressive Party. Woodrow Wilson, a Democrat, won the election that year.
In 1896, the state went for William Jennings Bryan, a Democrat. Republican William McKinley won the presidency.
South Dakota has had one U.S. House representative since 1983. At its peak, there were three from 1913-1933. Electoral votes are a combination of senators and representatives in Congress.
This fact brief responds to conversations such as this one.
Sources
The American Presidency Project, 1964, 1936, 1932, 1912, 1896
270towin.com, South Dakota
National Archives, Distribution of electoral votes
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