Again, the wikipedia link says nothing about the claim you're making except that a Texas school board controversially tried to promote it in its curriculum.
From further reading, the claim itself seems to originate from an Ann Coulter book.
The decrypted messages gave important insights into Soviet behavior in the period during which duplicate one-time pads were used. With the first break into the code, Venona revealed the existence of Soviet espionage[23] at Los Alamos National Laboratories.[24] Identities soon emerged of American, Canadian, Australian, and British spies in service to the Soviet government, including Klaus Fuchs, Alan Nunn May, and Donald Maclean. Others worked in Washington in the State Department, the Treasury, Office of Strategic Services,[25] and even the White House.
The messages show that the U.S. and other nations were targeted in major espionage campaigns by the Soviet Union as early as 1942. Among those identified are Julius and Ethel Rosenberg; Alger Hiss; Harry Dexter White, the second-highest official in the Treasury Department; Lauchlin Currie,[26] a personal aide to Franklin Roosevelt; and Maurice Halperin,[27] a section head in the Office of Strategic Services."
McCarthy's claims were far broader than that (and virtually all spurious). From a specialist historian:
> But if McCarthy was right about some of the large issues, he was wildly wrong on virtually all of the details. ... virtually none of the people that McCarthy claimed or alleged were Soviet agents turn up in Venona. ... The new information from Russian and American archives does not vindicate McCarthy. He remains a demagogue, whose wild charges actually made the fight against Communist subversion more difficult.
And read the link I originally shared more carefully this time.