Public policy is both an art and a craft.
It is an art because it requires insight, experience, creativity, and imagination in identifying social problems and describing them, in devising public policies that might alleviate them, in finding out whether these policies end up making things better or worse.
It is a craft because these tasks usually require some knowledge of economics, political science, public administration, sociology, law, and statistics. Policy analysis is really an applied subfield of all these traditional academic disciplines.