Political science, as you probably know, is a social science, allied with psychology and sociology.
Psychology is commonly regarded as somewhat...shall we say "flaky"?...because it's hard to accurately measure and analyze emotions, cognitive biases, etc. Political "science" is even crazier because philosophy (notably ethics) and opinion are such important components.
Trying to make political philosophy and opinion scientific is probably a lost cause, but we can at least endeavor to create a framework based on facts.
For example, we know that the Romans conquered other peoples, building an enormous empire. We know that John F. Kennedy was assassinated, Libya was invaded by NATO and West Virginia was created out of Virginia during the Civil War era.
We could list thousands of other facts, then connect related facts, similar to a connect-the-dots exercise. Hillary Clinton is thus linked to Walmart and the invasion of Libya.
I don't know if one could classify a collection of facts linked together as science, but it does give us a good starting point - somewhat analogous to an evolutionary biologist's tree of life.
We can now bring other tools into play, like historical patterns. The first great empires arose thousands of years ago. The Greeks built a notable empire that was eclipsed by the Roman empire. During the colonial era, the Spanish, French and British ruled ever bigger empires. Today, the U.S. effectively rules the biggest empire ever.
Which brings us to measurement. We can measure various historical events using a traditional time scale (hours, years, etc.). But how can you measure freedom or corruption?
Even if precise measurements are impossible to obtain, we can make comparisons and chart relative values. Thus, the United States is arguably more democratic now than it was when slavery flourished. On the other hand, U.S. citizens in general have lost many of the rights they enjoyed two centuries ago. That obviously complicates what turns out to be an overly simplistic view, but the same general idea applies.
Another thing that makes political science relatively unique is propaganda. Propagandists have certainly taken a bite out of science and philosophy, but the political arena is ground zero for propaganda.
This leaves us with an ironic predicament: In order to make politics scientific, we need to exorcise the propaganda that is almost synonymous with politics.
This can be achieved in part by simply brainstorming strategies for distinguishing between truth and propaganda.
In summary, political science will never be a precise science like mathematics, but it isn't a lost cause. Scientific principles can indeed by applied to the political arena.
I should also mention political principles, which often take the form of maxims (e.g. "Power corrupts and absolute power corrupts absolutely").
Such principles may be generalities, similar to other scientific principles, but they help us make sense of things.
So we have a framework made up of countless facts, a series of political principles and various tools for measuring and comparing things.