For projective, non-uniruled varities, the birational automorphism group is given a scheme structure in "Hanamura: Structure of birational automorphism groups, I: non-uniruled varieties". In particular the automorphism group is then a subscheme of that. There might be more straightforward treatments, dealing with the automorphism group only and maybe for all schemes generally.

For projective, non-uniruled varities, the birational automorphism group can also be given a scheme structure. The reference is "Hanamura: Structure of birational automorphism groups, I: non-uniruled varieties". As one expects, the automorphism group will be a subscheme of that.