Missouri Sen. Josh Hawley slammed Twitter's new privacy policy and said it leaves more room for the tech giant to censor conservative voices on "Fox News Primetime" Tuesday. 

"We ought to break them up," Hawley said. "At the end of the day, here's the deal: The last thing America needs is another Big Tech robber baron who doesn't care anything for free speech, and that's exactly what Twitter is giving us."

(Photo by Tom Williams-Pool/Getty Images)

WASHINGTON, DC - SEPTEMBER 29: Sen. Josh Hawley, (R-MO) speaks during a Senate Judiciary Committee hearing to examine Texas's abortion law on Capitol Hill on September 29, 2021 in Washington, DC. (Photo by Tom Williams-Pool/Getty Images) ( (Photo by Tom Williams-Pool/Getty Images))

If it receives a report about an "unauthorized private media," Twitter can now take action against pictures posted without explicit consent, even if said image is "shared without any explicit abusive content." The move comes right after its former CEO, Jack Dorsey, stepped down

SEN. JOSH HAWLEY ON CENSORSHIP, SECTION 230 AND DEMOCRATS' 'LOVE' FOR BIG TECH

Jack Dorsey former Twitter CEO cryptocurrency event

Jack Dorsey at the Bitcoin 2021 Convention, a crypto-currency conference held at the Mana Convention Center in Wynwood on June 04, 2021 in Miami, Florida. (Photo by Joe Raedle/Getty Images) (Photo by Joe Raedle/Getty Images)

"The misuse of private media can affect everyone but can have a disproportionate effect on women, activists, dissidents, and members of minority communities. When we receive a report that a Tweet contains unauthorized private media, we will now take action in line with our range of enforcement options," Twitter said in a Tuesday statement. 

"I promise you what it won't mean, the people whose privacy won't be protected are normal Americans who want to express their views, particularly if they have conservative views. I promise you that their privacy won't be respected, they'll still get censored," Hawley said. 

Twitter app on phone

This April 26, 2017, file photo shows the Twitter app icon on a mobile phone in Philadelphia. Twitter said Thursday, July 11, 2019, that it is investigating a problem with its service. Users across the U.S. and elsewhere are not able to access Twitter. (AP Photo/Matt Rourke, File) ((AP Photo/Matt Rourke, File)

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"It's the classic what's become the rule of the left, which is rules for thee, but not for me … They don't follow their own standards – they never do. Here's the other thing about Twitter: It doesn't really matter what they write down. They don't follow any of the rules anywhere. They just make it up as they go along. And the worst part is you can't go to court to enforce it. Currently, Twitter has immunity, so if they violate their Terms of Service as to you, there's nothing you could do about it. We should change that. You should be able to go and sue in court. And the other thing we ought to do is we ought to break them up."

Hawley also put Twitter's new privacy policy in the context of how Twitter makes its money. Twitter tracks its users' private phone use. 

"Let's just remember what Twitter does … to make their money. They track us around the web, everywhere they go, everywhere we go, they collect a dossier on us. They sell our information, they profit off of us. I promise you, they're not going to stop doing any of that stuff."