As far as I know, the demarcation problem has not been solved which makes answering this question "correctly" impossible.

That being said, (modern) economics is typically referred to as as "social science" and operates how I expect most people expect a science to operate. Namely, formulating hypotheses and models, testing them using data, and throwing out the theories that turn out to be wrong.

The process is, of course, much messier than a physical science like chemistry or physics for many reasons. The largest is that it is unfeasible and/or unethical to run many controlled experiments that one might want to run.

Same question can be asked for politics.

If you say is the economy a science the answer would be: NO

If you say is the parliament or congress a science the answer would be: NO

But if you would ask is the reasoning behind certain actions, the way of working/thinking, the way of policy building, the way of managing, the different ideas and concepts in economics and politics are those science?: the answer would be: Yea