WASHINGTON—President Donald Trump’s approval rating edged higher during a week in which he faced withering criticism following a summit with Russian President Vladimir Putin, signaling that he is positioned to weather the latest controversy sparked by his unusual brand of politics.

Mr. Trump’s job approval rating rose to 45% in a new Wall Street Journal/NBC News poll, the highest mark of his presidency and up 1 percentage point from June. The survey was taken over a four-day period that started July 15, a day before Mr. Trump’s...