An AI can easily start nuclear war, as can a human.

The only thing preventing a nuclear disaster are all the institutional measures limiting its accessiblity.

If you gave a single human (or a single AI) access to a magic no-strings-attached 'Send a Nuke' button, either the human/AI is the second coming of Jesus Christ, or a nuke will befall some unlucky portion of the population sooner or later. Bonus points if people can talk to the AI or if access to the button is hereditary.