without getting too deep into "field purity" [0], it's certainly a field of study insofar as game theory, psychology, anthropology, etc. are fields of study. It's possible to make certain models of behavior or outcome potentials, but running experiments is significantly more difficult than e.g. physics or biology.
So it's science inasmuch as anything with n=1 repeatability can be science
Astrophysics cannot make experiments either, but it's a (most fascinating) science indeed.
Weirdly, it's much easier to run empirical experiments in psychology (my field), but economics for whatever reason is MUCH more rigorous and empirical than psychology in my experience.
It may have to do with the overall complexity being easier to effectively model. Psychology has such big error terms that you either give up or get comfortable with a lot of hand-waving and dogma. A huge proportion of psychologists are just activists and have no real interest in being scientists (beyond the prestige).