What is 'rational choice theory"and its relationship with political science?

What a question! Rational choice theory is not a theory, and political science is not a science. Rational choice theory is the assumption that individuals always make prudent and logical decisions. These decisions provide people with the greatest benefit or satisfaction — given the choices available — and are also in their highest self-interest. Most mainstream academic assumptions and theories are based on rational choice theory, according to www.investopedia.com/terms/r/rational-choice-theory.asp

Science is based on observations. Even a casual observer notices that people seldom act in any "prudent and logical" manner. Political actions are often totally bonkers.