Mr O'Rourke made the statement on Twitter while imploring citizens not to "let him off the hook" for his involvement in the US Capitol riots.
"Don’t let him off the hook. Don’t let him make this about “Hollywood” — this is about Ted Cruz aiding and abetting an insurrection that killed 5 people including a cop and very nearly ended in the murders of members of Congress and the Vice President," Mr O'Rourke said.
Mr Cruz has been in a days-long Twitter spat with actor Seth Rogen. Mr O'Rourke thinks Mr Cruz has been engaging in that spat because it distracts the public from his connection to the insurrection.
"Why does he keep this fight going with Seth Rogen even though he's getting destroyed at every turn? Because he's guilty of sedition. He's hoping distraction & time diminish the urgency of accountability. Don't let him change the channel or the subject, it is sedition every time," Mr O'Rourke said.
Mr Cruz faced pressure to resign from lawmakers, the public and in the media for leading an effort in the Senate to overturn to the legal results of the 2020 election, which led to a mob attacking the US Capitol.
One rioter, who was caught with "homemade napalm" that was likely meant for use as Molotov cocktails, was arrested while in possession of a folder with Mr Cruz's Texan office phone numbers scrawled across the front.
Another protester was caught on video leafing through confidential Senate documents during the attack at the Capitol and saying "Ted Cruz would want us to do this" to his friends.
A video from the day before the attack on the Capitol shows Mr Cruz whipping up Trump supporters, telling them "we will stand shoulder to shoulder with you as we defend the United States of America, we won't go quietly into the night, we will defend liberty."
US Rep. Alexandria-Ocasio Cortez said Mr Cruz and fellow Senator Josh Hawley, who also led the charge to overturn the election, should resign or be removed.
"Sen. Cruz, you must accept responsibility for how your craven, self-serving actions contributed to the deaths of four people yesterday. And how you fundraised off this riot," she said. "Both you and Senator Hawley must resign. If you do not, the Senate should move for your expulsion."
Sen. Joe Manchin said earlier in the month that any members of Congress who were found to have aided or incited the US Capitol riot should face potential removal from office under the 14th Amendment.
In addition to lawmakers calling for Mr Cruz's resignation, the editorial boards of The Houston Chronicle, El Paso Times and the San Antonio Express News have called for him to leave office.
Mr Cruz issued a statement in the wake of the insurrection, calling it a "despicable act of terrorism and a shocking assault on our democratic system."
He then went on to explain why he was challenging the US's democratic system.
"That's why my colleagues and I called for an electoral commission to give Americans confidence in this past election and in elections going forward," he wrote. "It was the right thing to do. I very much wish Congress had not set aside these concerns, but I respect the position each of my colleagues took."