Let's define a few terms and that should largely answer the question. In the broadest sense, the term science means
... a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
In centuries past, science and the study of science was actually very closely linked with philosophy, with both fields of study being centered around answering some of the most basic questions of the nature of the universe and the world around us.
In more recent times (particularly the late 19th and 20th centuries), the term science has come more to specifically mean natural science, or the study of the natural world and phenomena that can be qualitatively measured through the scientific method and also quantitatively measured through mathematical data and analysis. The term natural science can also be thought of as dealing with physical sciences, or the study of the physical universe. This covers the classic areas of study like chemistry, biology, physics, geology, and astronomy.
Another more recent division of the term science is the term social science. This is meant to separate the previously mentioned natural sciences from other areas of study less concerned with the natural world and more concerned with human behavior, thought, and interaction. Areas of study in this realm include sociology, anthropology, economics, psychology, and political science. Mathematical data are still used to quantify and study patterns, but the subject matter is less tangible and more abstract in nature (thoughts versus physical objects). Specifically, political science is the subset in this area that studies politics, government, and bodies of law that govern human societal interactions.
So the answer to your question does depend a bit on your specific point of view. In the most broad and classical sense, political science is indeed a science. But in the more modern, compartmentalized context, political science would best be considered a social science.