Yes, the term is applicable to theology. Let's break it down to see why.
The first word is science. At its root, the word simply means knowledge. Many people forget that and the word has been somewhat hijacked to mean exclusively study about the natural world derived from facts and experiments, or more properly, the scientific method. The scientific method is a science in its own, but it is not science in whole.
The second word is faith. First, the word simply means having complete trust in something. You can have faith in just about anything, and hopefully you would have a reason to do so. I can have faith in a person to do the right thing, which might be based on our shared experiences. I can have faith in the scientific method to provide the best current understanding about something, which might be based on the history of its use. And, of course, I can have faith in God, that he is there and cares about us, that he will keep his word, that Christ will return, and that eternal life awaits for those who love Him. This can be based on any number of things including, apologetics, being convinced the Gospels and New Testament are true, and personal revelation. Again, many people forget that the word has been hijacked to mean believe without reason, or what is colloquially called blind faith. The word simply does not mean that and that phrase and the actually definition of faith are contradictory. In short, faith means believing in what you have reason to believe.
So the phrase the science of faith means exactly knowledge of what there is reason to believe. Specifically, in this context, the author means exclusively items concerning Christianity and the Christian God. So alternatively, the author may mean knowledge of the Christian religion with assumptions that it is true at its core. Slightly different than what I have come up with, but acceptable and understandable considering the time and place that he said that.