The definition of science, according to Oxford Advanced Learner's Dictionary is:
knowledge about the structure and behavior of the natural and physical world, based on facts that you can prove, for example by experiments
Science is subjects about the natural and physical world that are empirically to explain how it works and what its effects are. Linguistics is the study of the natural and physical phenomenon of human language. Therefore, it classifies as a science.
Linguists generally study how words are formed, how they sound, and why they are used. They study the larynx, the tongue, the vocal cords, and the diaphragm, all of which are interconnected and used when we speak. They take special note of nasal tone, inflection, diction, and clarity. They are especially interested in regional dialects and colloquialisms, and are so good at what they do that they can listen to a person speak and tell immediately where they're from.
An example proving that linguistics is a science is that most colleges and universities around the country offer majors in various branches of Linguistics. According to http://www.lsadc.org/info/ling-faqs-whymajor.cfm, linguistics is a valuable tool to help establish, strengthen, and understand how man communicates and why language is so important.