The conservative Republican senator said he will withhold judgment about her nomination until she testifies before the Senate.
As one example, his office pointed to a decision last year when she sided with the city of New Haven, Conn., in a discrimination case brought by white firefighters. The city threw out results of a promotion exam because too few minorities scored high enough. Coincidentally, that case is now before the Supreme Court.
That ruling has drawn criticism from other conservatives as well, and is likely to play a role in her confirmation hearing.
DeMint said he looks forward to meeting with Sotomayor and learning more about her judicial approach.
"Few things are more central to our duty than confirming Supreme Court justices who will uphold the law and apply it equally for all Americans, not rewrite it from the bench based on personal opinion," DeMint said.
Obama announced his nomination of Sotomayor, who would be the country's first Hispanic Supreme Court justice, on Tuesday. She is an appeals judge for the 2nd U.S. Circuit Court of Appeals, which covers New York, Vermont and Connecticut.