Of course according to his religion, he better be; he’s supposed to be divine in some way. The BBC says: “Those who have met him describe an intense personal charisma.” I seem to remember that, in one of his books, Christopher Hitchens conceded the Dalai Lama had charisma. (To Hitchens, of course, the Dalai Lama is bad because he has something to do with religion.)
The Dalai Lama is chosen when he is a small boy by a group of monks, I think. (It’s sort of like the Jedi.) If charisma is an innate, rather than learned, characteristic, it would not be too much of a stretch to suppose that he had it even as a child, and that this led to him being picked.