In every science there are facts: facts and ideas; or, facts and the mind. Science is more than knowledge. Knowledge is the persuasion of what is true on adequate evidence. ... In every department the man of science is assumed to understand the laws by which the facts of experience are determined; so that he not only knows the past, but can predict the future. ... If, therefore, theology be a science, it must include something more than a mere knowledge of facts. It must embrace an exhibition of the internal relation of those facts, one to another, and each to all. It must be able to show that if one be admitted, others cannot be denied. [Charles Hodge, Systematic Theology (Peabody, MA: Hendrickson, 2001), p. 1]
What is true of other science is true of theology. We cannot know what God has revealed in his Word unless we understand, at least in some good measure, the relation in which the separate truths therein contained stand to each other. (Ibid., p. 2)
What does Charles Hodge mean when he claim that theology is a science? In the beginning of his Systematic, Hodge makes it clear what he means by that by comparing theology with other subjects like astronomy, geography, and other such subjects of study. Just like other subjects have facts which must be studied and put together in their relation to one another, so likewise theology consists of facts from the Bible to be put together in biblical truth.
From the analogy Hodge draws between theology and the other sciences, it can be seen that Hodge is calling theology a "science" using it in the older meaing of scientia, a word denoting that the subject is to be studied rigorously to gain knowledge. By calling theology a "science," Hodge means by that that theology belongs to the same genre of intellectual enquiry as other subjects like astronomy, geography or biology. They are all "sciences" in the sense that (1) all of them require intellectual rigor, (2) facts are present in all of them, and (3) these facts are not left by themselves but are to be put together into theories and relations to other facts.
A simple example of that from the Bible is when one reads 1 Samuel 15, and compare verse 10 and 29. Anyone who attempts to reconcile the two verses are taking the two verses ("facts") and parsing them out how is it exactly that both are true ("put together into theories and relations to other facts"). In other words, most Christians do some form of systematizing in their theology. The difference between Systematic Theology and what most Christians do is whether the "systematizing" is done properly and rigorously, or improperly and incoherently. But unless one claims that the two verses are both true and therefore the Bible is not the Word of God because it contradicts itself, or engage in other forms of Higher Criticism, Systematic Theology is inescapable. Also, the Bible is not Systematic Theology for the simple reason that Systematic Theology does the systematization of facts, not provides two texts that must be parsed in order to not be contradictory.
It is true of coure that Hodge further defines the method of theology as induction (Ibid., p. 8). We note here that this is in Section 2 of his first chapter, whereas defining theology as a science is in Section 1. That means that definining theology as science is a queustion to be dealt with logically prior to the nature of theological method. Therefore, whether theology is a "science" or not is independent of the question of theological method. One can, like me, accepts Hodge's definition of theology as a "science," while rejecting the idea that the method of theology is induction. One should not conflate the genre of theology with the method of theology, which are two different topics altogether.
Based on Hodge's discussion, I would certainly agree that theology is a "science." Of course, theology is more than a "science," since it involves the will and the emotions as well, but it not less than that.