It does not give a specific date, although it is said sometime after the unification of the United States and British commonwealth.
The splitting up of the world into three great super-states was an event
which could be and indeed was foreseen before the middle of the twentieth
century. With the absorption of Europe by Russia and of the British Empire
by the United States, two of the three existing powers, Eurasia and
Oceania, were already effectively in being. The third, Eastasia, only
emerged as a distinct unit after another decade of confused fighting.
-- Part 2, Chapter 9
However, the book gives some clues, saying there was an atomic war in the 1950s and shortly after the Revolution followed.
Although the Party, according to its
habit, claims the invention for itself, atomic bombs first appeared as
early as the nineteen-forties, and were first used on a large scale about
ten years later. At that time some hundreds of bombs were dropped on
industrial centres, chiefly in European Russia, Western Europe, and
North America. The effect was to convince the ruling groups of all
countries that a few more atomic bombs would mean the end of organized
society, and hence of their own power.
-- Part 2, Chapter 9
Quote from Wikipedia:
Oceania, the fictional superstate in George Orwell's Nineteen Eighty-Four, appears to have emerged from a formal political union of the United States and the countries of the British Commonwealth, which later annexed the remainder of the Americas. Big Brother and Emmanuel Goldstein, fictional characters from the book, led the Party to power in Oceania after a revolution of some kind. After the Party achieved control of Oceania, Ingsoc became the official governing ideology and other political beliefs were increasingly marginalized. Goldstein and Big Brother later became enemies and differed in their interpretation of Ingsoc. Goldstein was eventually branded a criminal and was used as a symbol of treachery and sedition by the party.
