This is probably "Returning Home", by Ian Watson, published in Sunstroke and Other Stories (1982), and also in Omni (December 1982). In this story, the USA develops a "Super-Radiation Bomb", which kills living things but leaves property intact, and the USSR develops the "Socialist Bomb" (SOB), which destroys property but not people:
In other words, drop an SOB on New York City and very soon you would have no New York City at all, only an empty space with millions of people wandering around stark-naked. ...
Then there is a brief war:
In less than an hour the U.S.A. and the USSR exchanged their entire arsenals of Radiation Bombs and SOBs.
The Americans migrate into the now empty Russia, but the land somehow Russifies them:
... I know—for a fleeting moment—that every building and machine and thing we use is alive, possessed. Locomotives, gastronoms, buses and tractors, offices and ice-cream carts and rouble notes, all tell us what to do, and the way to do it. The whole environment, of Russian making, sucked up their souls for safekeeping, and now they have entered us, like dybbuks. ...
...
America is as wild and empty and far away as it was a hundred thousand years ago before any Asians first traversed the Bering Strait to roam the American plains as Indians. America is a forgotten country. Mother Russia is our land, and we are hers.
