CARACAS, Venezuela—President Trump’s trade and other foreign policies have made him unpopular in many countries that are traditionally U.S. allies. But they love him in Venezuela.

Polls show that the U.S. government’s toughening stance against Venezuela’s authoritarian regime in recent weeks has catapulted Mr. Trump up the popularity rankings in the crisis-stricken South American country. His favorable numbers are especially noteworthy in a region that has long been wary of American intrusion.

Protesters...