Dictionaries differ on this matter, but most dictionaries seem to say that 'born' is a past participle form of a verb, not an adjective. Cambridge Dictionary seems to be in the minority.
That said, it's hard to determine which dictionary should be followed. I think it entirely depends on how you define 'verb' and 'adjective'.
In my own dictionary, I think it's a verb always in the passive construction. There are some verbs that are predominantly used in the passive construction, so it wouldn't be too idiosyncratic to think of 'born' as one such extreme case.
The reason I don't think it's an adjective is because it is normally used in the past tense of the verb 'be'.
He was born in the States.
If 'born' were an adjective, it should be describing an attribute of 'He' rather than an event. But it is describing an event, not an attribute, in part because the past tense 'was' should be used in the sentence. The event of him being born occurred in the past, so the 'be' has to be in the past tense form. Hence, the impossibility of the following:
*He is born in the States.