There have been many questions about what the Ring would do to various beings of Middle Earth. In general It takes control of whatever it is through tempting them with power. There is some suggestion that the Valar are too powerful for it to affect them (or at least that they are too wise to fall for its tricks).
Morgoth is neither powerful (in most conventional ways, as he is during the events of the story) nor wise. He is, however, Sauron's master and, unlike Sauron, his goal is mostly destruction rather than domination. Would the Ring further corrupt him? Dilute his malevolence? Be corrupted further by him? Could it provide him with some of the strength that he had squandered (after all, wasn't the point of the Ring to stop the same thing from happening to Sauron)?
Is there simply not enough information available to know?
While I am also interested in whether it would even be possible to get the One Ring to Morgoth, that is a different question.