In his now-infamous July phone call with Ukraine's president , President Donald Trump referred briefly to a long- discredited conspiracy theory that tries to cast doubt on Russia's role in the 2016 hacking of the Democratic National Committee.

Some Trump backers who circulate unsubstantiated rumors have latched onto some version of the theory to support claims he's being persecuted by "the deep state," also known as the federal bureaucracy, as the House of Representatives begins an impeachment inquiry.

In broad outline, the theory contends — without evidence, of course — that the DNC hack was...