WASHINGTON — Senator Rand Paul, Republican of Kentucky, on Wednesday filed a lawsuit against President Obama and the leaders of several intelligence agencies. The suit challenges as unconstitutional the National Security Agency’s once-secret program that is collecting bulk records about Americans’ phone calls.

Mr. Paul, who had announced his intention to file the lawsuit in early January, joins an increasingly crowded set of plaintiffs, with several similar cases already pending.

But because of Mr. Paul’s status as a rising star of the Tea Party faction of the Republican Party — one who staged a nearly 13-hour filibuster on the floor of the Senate in March raising concerns about the rules governing “targeted killings” using drone strikes — his lawsuit may attract particular attention.

“Today we ask the question for every phone user in America: can a single warrant allow the government to collect all your records, all the time?” Mr. Paul said in a statement. “I don’t think so.”