Senator Lindsey Graham said he was informed three months before the November 8 presidential election that his accounts were broken into.
"Our campaign vendor was hacked. We were told by the FBI in August that we were hacked in June," he told CNN television.
Trump has rejected the conclusion by the CIA and FBI that Russians stole data out of campaign computers and were behind the leak of documents and communications from the Democratic National Committee and the emails of Democratic candidate Hillary Clinton's campaign chief, John Podesta.
Those leaks damaged Clinton's ultimately losing campaign effort and the CIA concluded that, with the leaks, Russia had intended to bolster Trump.
"I do believe the Russians hacked into the DNC. I do believe they hacked into Podesta's email account. They hacked into my campaign account. I do believe all the information released publicly hurt Clinton, didn't hurt Trump," Graham said.
Comment: Your feelings and beliefs are irrelevant, you opportunistic hack.
"But I don't think the outcome of the election is in doubt," he added.
Graham, a member of the Senate Armed Services Committee, has called for a congressional probe into Russian election hacking.
And he said on Twitter that Russia would pay.
"My goal is to put on President Trump's desk crippling sanctions against Russia. They need to pay a price," he said.
Separately late Wednesday Devin Nunes, the chair of the House Intelligence Committee, said that the main intelligence community agencies had rejected his demand that they brief the committee on Thursday on cyber attacks during the election.
"The committee is vigorously looking into reports of cyber-attacks during the election campaign, and in particular we want to clarify press reports that the CIA has a new assessment that it has not shared with us," he said in a statement.
"The committee is deeply concerned that intransigence in sharing intelligence with Congress can enable the manipulation of intelligence for political purposes."
“Free speech is a great idea, but we’re in a war.”
“We need to raise taxes to get our nation out of debt.”
“I’m a Verizon customer. I don’t mind Verizon turning over records to the government if the government is going to make sure that they try to match up a known terrorist phone with somebody in the United States. I don’t think you’re talking to the terrorists. I know you’re not. I know I’m not. So we don’t have anything to worry about.”
"And when they say, ‘I want my lawyer,’ you tell them, ‘Shut up. You don’t get a lawyer.'”
“I think TARP I was necessary because the whole economy was going to collapse and Bernanke, Paulson, and everybody that I know and quite frankly trust, after Lehman brothers went down, that if we had not involved ourselves quickly you’d have a financial meltdown.”