Following the 1991 dissolution of the Soviet Union, Belarus, Kazakhstan, Russia and Ukraine ratified the treaty and took on its obligations.
The Heritage Foundation chimes in here:
THE ABM TREATY WITH RUSSIA: THE TREATY THAT NEVER WAS
A much better argument, and interesting to read, but not related to the question of how treaties may be terminated under the Constitution. I believe, based on my reading of the arguments, that Congress should do it.