A statement from a staff member said he was in quarantine but remained asymptomatic.
As US senators work on a multi-trillion-dollar rescue package to help the US economy hit hard by the pandemic, Paul has at least twice voted against such emergency funding.
Paul, who is 57, is the third member of Congress known to have contracted the virus. Two members of the House of Representatives — Ben McAdams of Utah and Mario Diaz-Balart of Florida — earlier announced positive tests.
Paul, the junior senator from Kentucky, “is feeling fine and is in quarantine. He is asymptomatic and was tested out of an abundance of caution due to his extensive travel and events,” said the statement from his staff.
It said Paul was not aware of any direct contact with an infected person. It added that the senator’s Washington office had begun operating remotely 10 days ago, so “virtually no staff has had contact with Senator Paul.”
It was not clear exactly when he was tested.
On Wednesday, Paul voted against a $100 billion stimulus package designed to combat the virus.
The bill, which passed by a 90-8 vote, called for free virus testing and paid sick leave for some displaced workers.
The senator, a deficit hawk, argued that Congress should pay for the measure by cutting funding for wars or other “frivolous” programs, the Louisville, Kentucky Courier-Journal reported.
He urged his colleagues to “stop being a rubber stamp for wasteful spending.”
Earlier in the month, he opposed a bipartisan $8 billion plan for emergency coronavirus funding.