The possible Republican presidential candidate told reporters outside the courthouse his class action suit could involve millions of U.S. residents, everyone who uses a phone, NBC reported.
The NSA's massive surveillance program demands the records of phone calls from telecommunications companies, without a warrant. The program doesn't look at content, but digitally checks whether a call is to a foreign or domestic terror suspect.
Paul, from Kentucky, said he would take his case all the way to the U.S. Supreme Court to determine "whether a single warrant can apply to the records of every American phone user all of the time, without limits, without individualization."
"We fought the American Revolution because we were unhappy about British soldiers writing generalized warrants. We wrote the Fourth Amendment to be specific to the person, to the place and to the items," Paul said.
"I'm not against the NSA; I'm not against spying; I'm not against looking at phone records. I just want you to go to a judge, have a person's name and individualize the warrant. That's what the Fourth Amendment says."
Paul's lead counsel in the case is Ken Cuccinelli, former Virginia attorney general who lost the election for Virginia governor last year. Cuccinelli said suit seeks an order stopping the NSA from its phone data collection and a purge of five years' worth of records, NBC reported.
Notable deaths of 2014 [PHOTOS]