WASHINGTON—A year ago, GOP Sen. Orrin Hatch was defending big tech firms against liberals who want to punish them for anticompetitive conduct, deriding the idea as “hipster antitrust.”

Last week, the Utah senator appeared to throw in with the tech industry’s critics. In a letter to the Federal Trade Commission, Mr. Hatch called for the agency to investigate Google, a unit of Alphabet Inc., for possible antitrust behavior that he called “disquieting.”

For...