Historically, he was the vassal of Charlemagne and then the early Holy Roman Emperors, at least something of a vassal. You would need a special event, but if you are an emperor, you would need to have a vassalization CB or a decision or event to force the issue. Of course Italian unification just left the Pope with one barony in CK2 terms, so it might be possible to take Rome that way

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Now to be brief: you need to make a decision or event (set_de_facto_liege I think is the right syntax); you might want to change the entry for the Papal states in landed_titles that says <independent = yes> preventing a simple diplomatic action (afaik); and remember that if you take all his land he will exist anyway. It should bug the other Catholic rulers that you are liege of the Pope. Anti-popes and heresy spread during the Avignon Papacy for example. But maybe it will be acceptable.
It will also mean an end to crusades and invasion CBs, as the religious head has to be independent for those to work.