On Tuesday, the committee released a report on the impeachment inquiry which included records of calls from Nunes, presidential lawyers Rudy Giuliani and Jay Sekulow, journalist John Solomon, Fox News host Sean Hannity, a Giuliani connection Lev Parnas, and other White House associates.
Schiff subpoenaed both AT&T and Verizon for the information. The act has sent a chill among Republicans concerned about the chairman's reach.
Appearing on "Tucker Carlson Tonight" with host Tucker Carlson, Nunes said Schiff's actions were unprecedented.
"They have now set a precedent where Adam Schiff can go get any phone number he has to AT&T and AT&T is going to comply," Nunes explained.
Carlson asked if there was a limit to Schiff's power as chairman: "Can he get my email, too?"
"If you look at what he did then, it's not just the president's phone records -- okay -- or the president's lawyer's phone records, he also was able to get a journalist who they hate...who they say is a conspiracy theorist," said Nunes. "And, he was able to figure out that that was John Solomon's phone number."
"Then, he was able to get my number, right? And, because I had talked to Rudy Giuliani and somehow that's now a crime, and then I make it into his report," Nunes explained further.
"And, we have to remember....we spent the last three years, at first if any Republican ever talked to any Russian at any time -- even if you are Russian-American -- that was a no-no. Then we were criticized," he continued. "We switched to Ukraine. If you talk to any Ukrainian that's now a crime. Now, I can't even talk to Rudy Giuliani who I have known for 10 years. That's supposedly a crime."
Nunes is currently suing CNN for defamation after journalist Vicky Ward reported claims that he had met with Ukranian prosecutor, Viktor Shokin, in Vienna in 2018 to dig "up dirt" on Hunter and Joe Biden.
"So, this is -- this is wrong," Nunes said. "And, what is happening -- whatever is happening in this town is wrong."
He pledged to look at "whatever legal remedies I have" because "I actually have some civil rights here, too."
The top spokesman for Democrats on the House Intelligence Committee said Thursday that they "did not subpoena call records for any member of Congress or their staff...or for any journalist."
"Any questions about the fact that Members, congressional staff, or journalists appear in call records released by the Committee should be directed at those individuals, who were in contact with individuals of investigative interest to the impeachment inquiry," Patrick Boland told The Daily Beast.
Fox News' Brian Flood, Nick Givas, and Brooke Singman contributed to this report.