The chords in a song of a particular key are predominantly members of the key’s scale. I imagine you could get a good approximation statistically (if there is enough data) by comparing the predominant accidentals in the chords listed to the key signatures of the keys.
See https://en.wikipedia.org/wiki/Circle_of_fifths
Of course, a song in any key can/will have accidentals not in the keys scale, so it would likely be a statistical approximation. But over several bars, if you add up the accidentals and filter out all but the ones that occur most often, you may be able to match to a key signature.
Addendum: as Jonas w correctly points out, you may be able to get the signature, but you won’t likely be able to determine if it is a major or minor key.