WASHINGTON—Texas Democrat Beto O’Rourke plans to test the strength of his party’s newfound populism in a longshot 2018 Senate campaign against Republican Sen. Ted Cruz.

Mr. O’Rourke, a 44-year-old, three-term congressman from El Paso, on Friday became the first major Democrat to announce a challenge to a Republican senator facing re-election in 2018. His entry in the race against a heavily favored incumbent is the latest sign Democrats feel emboldened under GOP President Donald Trump.

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