Sounds like the 1966 book [Colossus][1], by D F Jones.  The Americans create a supercomputer to run the national defenses, but it discovers an equivalent Russian computer, links with it, and takes over the world.

[![enter image description here][2]][2]


  [1]: https://en.wikipedia.org/wiki/Colossus_(novel)
  [2]: https://i.sstatic.net/bqii6.png