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The result? Mr. Trump more than ever dominates U.S. Iran policy; contending political factions within the administration and outside it must jockey for his support. And the more he talks and tweets about Iran, the less clear anyone is about his ultimate intentions.

None of this should be surprising. Consistently inconsistent on issues from trade with China and immigration from Mexico to Venezuela and North Korea and now Iran, Mr. Trump has been by turns more hawkish than any of his predecessors and dovish enough to thrill Sen. Rand Paul.

This president is first and foremost a showman. From his early real-estate days in 1970s New York through his time in reality television and into his third career in politics, Mr. Trump has understood and shrewdly deployed the power of fame. He has turned American politics into the Donald Trump Show, with the country and the world fixated on his every move, speculating feverishly about what will come next. Whether threatening on Twitter to rain down destruction from the sky, reining in the dogs of war at the last minute, or stage-managing high-stakes summit meetings, he is producing episodes of the most compelling reality show the world has ever seen.

Whether this helps or hurts American foreign policy is another question, but to turn intractable foreign-policy problems like North Korea’s nuclear program into fodder for the Trump publicity machine represents a triumph of marketing ingenuity if not of national strategy. Unresolved foreign-policy crises normally weigh on a president’s popularity; in Mr. Trump’s case, they become plotlines that provide drama and suspense. When Kim Jong Un gives him lemons, Mr. Trump sets up a lemonade stand.

The president’s critics continue to dismiss him as a cable-TV-obsessed, narcissistic know-nothing even as he dominates American and world politics. What they miss is that Mr. Trump not only possesses an instinctive ability to dominate media coverage; he is also a keen judge of power. The fashionable neighborhoods of Los Angeles are filled with world-famous celebrities who yearn for political power; Hollywood hates him so virulently in part because, like Ronald Reagan, Mr. Trump has transcended show business and transformed celebrity power into the real thing.

The key to the president’s Iran policy is that his nose for power tells him Iran is weaker and the U.S. stronger than the foreign-policy establishment believes. President Obama’s nuclear deal, from Mr. Trump’s perspective, was the result of a successful Iranian con game executed by clever Islamic Republic negotiators who ran circles around John Kerry. What Mr. Trump wants is a deal with Iran that matches his sense of the relative power of the two countries.

In pursuit of this goal he is combining two sets of strategies. At the level of public diplomacy he is engaging in his standard mix of dazzle and spin, shifting from bloodcurdling threats to gentle billing and cooing as need be. And at the level of power politics he is steadily and consistently tightening the screws on Iran: arming its neighbors and assuring them of his support, tightening sanctions, and raising the psychological pressure on the regime.

Mr. Trump well understands the constraints under which his Iran policy is working. Launching a new Middle East war could wreck his presidency. But if Iran starts the war, that’s another matter. A clear Iranian attack on American or even Israeli targets could unite Mr. Trump’s Jacksonian base like the attack on Pearl Harbor united America’s Jacksonians to fight Imperial Japan.

Americans did not want war in 1941. By levying crippling economic sanctions on Japan, President Roosevelt gave Tokyo the choice between retreating in Asia and launching a war against the U.S. Mr. Trump believes he can drive Iran into a similar corner—and that a weakened Iran will choose retreat over war.

Mr. Trump’s approach to American diplomacy horrifies an establishment that believes restraint, predictability and responsibility are the hallmarks of a global hegemon. Lesser powers can indulge in histrionic grandstanding, clownish antics, outrageous claims and public tantrums. The hegemon exhibits power by rising above such tawdry tricks.

This is not the Trump approach. A street fighter and a brawler, Mr. Trump uses the same tools in foreign policy as he does in politics at home. The jury is very much out on whether these techniques will bring lasting success, but no one should forget that staging riveting public spectacles has been a prime pathway to power since the days of ancient Rome.