The song is taken from her seventh studio album, Lover, the first new music released since her departure from Big Machine Records.
It takes aim at male music executives - in particular Scooter Braun, who purchased her back catalogue last year.
The credits stress the video was directed, produced and owned by Swift.
In the video, the lead character, in heavy prosthetics, stops to relieve himself against an underground wall which has been graffitied with the name of Swift's first six albums - all of which are owned by the Big Machine label.
Pinned to the wall is a poster reading: "Missing. If found return to Taylor Swift". Beside that is a "no scooters" sign.
It's the latest shot fired in her war with Braun, who she accused of attempting to "dismantle" her "musical legacy" after he bought Big Machine for $300m (£237m) last June.
In November, Swift claimed Braun and Big Machine founder Scott Borchetta had prevented her from performing a medley of her old hits at the American Music Awards.
They denied the claims, and the performance went ahead as originally planned.
Braun later pleaded with her to stop the public campaign against him, saying his family had received death threats.
The singer made a subtle nod to their spat while performing at the AMAs, where she won six awards including artist of the decade.
She took to the stage wearing a prison-style white shirt stencilled with the names of the albums in question, while performing new and old songs.
While receiving another artist of the decade award at the Billboard Awards, Swift called out Braun directly, saying her treatment had been "the definition of the toxic male privilege".
"The man" in the video bears more than a passing resemblance to Leonardo DiCaprio's character in The Wolf of Wall Street (the song references DiCaprio's playboy lifestyle), as he's congratulated for his business and sporting achievements and being the "greatest dad in the world", all while getting up to no good.
It's a thinly-veiled attack on the disparity between how men and women in the same roles are viewed by society.
The lyrics include the words: "I'm so sick of running as fast as I can / Wondering if I'd get there quicker if I was a man / And I'm so sick of them coming at me again / 'Cause if I was a man, then I'd be the man"
At the end of the music video, the director, real-life Taylor Swift, asks her male counterpart - voiced by Dwayne "The Rock" Johnson - if he could do it all again but this time make it "sexier".
Swift is likely to play the song when she headlines Glastonbury later this year.