I think INFJ or INTJ, from what I've heard about him, he is described as being dark, quiet, introverted, serious, and focused.

Some of the songs on the police album synchrinicity were influenced by Carl Jung's concept of synchrinicity( the idea that the experience of two or more seemingly causally unrelated events occur together in a meaningful manner) and Sting was the main lyricist for the police.

To me this points to Sting possibly being dom Ni .