As a (secret at the time) member of the Communist Party in USA (other references here) and considering his scientific platform, it is highly likely that he at least was being approached by recruiters from KGB (GRU).
If he eventually passed secrets to the Russians and became a spy, only the Russians would know as there exist no available evidence of such.
A letter from Boris Merkulov (USSR People’s Commissar for State Security) to Lavrenty Beria (USSR People’s Commissar for Internal Affairs), 2 October 1944 states:
In 1942 one of the leaders of scientific work on [uranium] in the USA,
Professor Oppenheimer while being an unlisted (nglastny) member of the
apparat of Comrade Browder informed us about the beginning of work.
Source: Cold War International History Project / Wilson Center
Analytics says the following about the letter and Oppenheimer -
Jerrold Schecter, a historian and journalist, writes this:
Why did the NKVD begin an effort to recruit Oppenheimer in 1944 if
Oppenheimer had already been working for the NKVD since 1942? The
answer is simple. Oppenheimer was never formally recruited as a Soviet
agent. He was asked, as a friend of the Soviet Union, to help the
American Communist Party obtain information on nuclear secrets.
Oppenheimer's role was that of a facilitator, which the document from
Merkulov to Beria notes in detail. ("provided cooperation in access to
research for several of our tested sources including a relative of
Comrade Browder." Sacred Secrets, pp.315-317). Soviet intelligence's
appeal to Oppenheimer and other Manhattan Project scientists was to
aid a wartime ally to build an atomic bomb before the Germans could
build their own.
Both the GRU and the NKVD wanted to recruit Oppenheimer after Kheifetz
and the Zarubins were recalled. However, their contacts were broken
when Earl Browder and the Communist underground, through Comintern
agent Steve Nelson, no longer could work directly with Zarubin and
Kheifetz. Kheifetz had served both as the NKVD and the Comintern
coordinator for Soviet espionage. When the Comintern was disbanded in
1943 Soviet intelligence was looking for a new channel to contact
And he concludes with:
Does Oppenheimer's cooperation make him a spy under American law? Yes,
if there is documentary evidence or testimony to back the assertion of
Oppenheimer's cooperation in Merkulov's letter to Beria. The Soviets
say Oppenheimer was helping a wartime ally, but they knew the
materials to which he provided access would make him guilty of
espionage if revealed and prosecuted. The Russians are still
protecting Oppenheimer's reputation. [...] President Putin admitted on
CNN's Larry King Live (September 8, 2000) that American scientists
cooperated in Soviet atomic espionage , but he did not name names.
Russian intelligence still protects its assets.
The Haunted Wood, by Allan Weinstein and Alexander Vassiliev. Weinstein, president of the Center for Democracy, and Vassiliev, a former Soviet agent who had access to KGB archives, write (p. 184):
The fact that station chief Grigory Heifetz was recalled to Moscow in
1944 because of his failure to bring any of 'Enormoz's' scientists
into the fold suggests, however, that Oppenheimer never agreed to
become a source of information for the Soviets, as some recent writers
In a footnote, Weinstein and Vassiliev cite an unpublished KGB document as the source for their conclusion: "File 25748, Vol. 2, pp. 116, 148".
Gregg Herken, a historian and curator at the Smithsonian Institution and author of "Brotherhood of the Bomb, conclude in his comment:
[...] the case for Oppenheimer as a traitor and a spy is not
convincing. Absent additional and better evidence, the question raised
by the Schecters deserves only a Scotch verdict: not proven. But if
the Schecters and their allies are indeed interested in pursuing the
truth about Kheifets and Oppenheimer, the KGB file cited by Weinstein
and Vassiliev might be a good place to start, the next time they are
Hayden Peake, formerly with U.S. Army intelligence, writes:
The authenticity of the so-called Merkulov letter in Scared Secrets
(reproduced on pp. 315-7) has been challenged by analysts who have
accepted as authentic another Merkulov letter cited in Weinstein's
Haunted Wood (pp. 183-84) which is neither reproduced nor scheduled to
available at any time for independent authentication. This may be
convenient but it is inconsistent.
Further he writes:
On the point of whether Oppenheimer was a source for the NKGB, the
letter states he was if one accepts that antecedent of the "he" in 4th
paragraph is Oppenheimer. Providing "cooperation in access to the
research" of "tested sources" to a man he knows to be a Soviet agent
or officer, makes Oppenheimer a knowing NKGB source. Whether one
wishes to call him an agent is semantic quibbling.
He close his comment with:
In short, I accept the letter and its implications.
So in conclusion: until the Russians choose to reveal if Oppenheimer actually worked for them, or informed them, there is no evidence that he did so. Are there indications? yes, was he interesting for the Russians? definitely, could Oppenheimer sympathies with Soviet? As member of the Communist Party it's likely he did.
But nevertheless, without solid evidence one remain innocent until proven guilty.
New papers has been declassified (3. Oct 2014) and may ad nuances to the story. They do not seem to provide solid evidence for the topic itself, but can be an interesting read by itself: