I believe that, yes, what we are experiencing in the US at this time can be defined as a cult of personality. We have a person who is, among other things, extremely narcissistic, who thrives on and demands flattery and praise from all those around him; who insists on the unwavering loyalty of his followers; who worships the ground he himself walks on and who, while being devoid of observable actual leadership skills, has become completely dependent upon his charisma (and fear, but that is another story for another time) to attain and maintain power.
The media has been instrumental in his reaching this status focusing on and reporting his every word or tweet. There is reason to believe that there is validation in the old saw that any publicity, even negative, is good publicity.
Being a person of some wealth, he has been rich enough and savvy enough to hire competent staff to not just promote those products he sells or produces but to actually push himself as the main product. Whether this is by marketing design or whether this comes from a sincere and deeply held personal belief that it truly is him that is worthy is unclear and by this time has become irrelevant. It is, or rather, he is what he has convinced others he is.
In addition we have others in power who are willing to bow down to him in order to further their own agenda (the enemy of my enemy is my friend) and their observable obsequiousness has brought further strength to his developed persona and helped convince others of the righteousness of his authoritarian actions and stance.
All this, the self-aggrandizement, the media blitz, the marketing strategy and the meek subservience of those already in power has brought us to this point where we have over 30% of the population believing that he is the messiah they have been searching for all these long years.