"We ought to break them up. 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," Hawley said during an appearance on "Fox News Primetime."
"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 statement Tuesday.
Hawley expressed that he is doubtful that Twitter's increased efforts to protect users will apply to conservatives who are targeted on the platform.
"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," Hawley said. "I promise you that their privacy won't be respected, they'll still get censored."
"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," he continued. "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 added that the social media giant is not going to stop tracking user data because that is how it makes its money.
"Let's just remember what Twitter does … to make their money," he said. "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."