Californians may have thought they were done voting on Gavin Newsom. He’s been elected twice as governor, defeated a recall seeking to oust him from office, and is barred by term limits from running again.

But the state’s voters will soon weigh in once more on Mr. Newsom’s fate. This time, it will be in the form of a ballot measure the governor is pitching as a way to go after President Trump.

Mr. Newsom on Thursday kicked off his campaign for a proposition asking California voters to approve a new congressional map, an extraordinary move meant to help Democrats win more seats in the U.S. House of Representatives to counter Mr. Trump’s request that Texas gerrymander five more seats for Republicans.

The governor gathered Democratic lawmakers and union leaders waving “Defend Democracy” signs in a Los Angeles auditorium for a show of solidarity, marked by the hopeful buzz of a campaign rally. The event was held a day before California lawmakers aimed to make the map public.

“On Nov. 4 in California, you have the power to stand up to Trump,” Mr. Newsom told the crowd. “You have the power to declare that you support a system that is not rigged.”

The governor has dubbed his measure the Election Rigging Response Act. The phrase was emblazoned on red, white and blue signs throughout the auditorium.