Virginians cast ballots Tuesday on a proposed congressional map that would aggressively gerrymander the state in the Democrats’ favor, giving the party as many as four extra U.S. House seats.

President Donald Trump has lied for years that elections Republicans lost fair and square were “rigged” by mail-in ballots.

Democrats are seeking to use their control of state government to redraw the state’s congressional map in a way that would add four more seats for their party, but they need approval from voters to do...