Yes, there is a Philosophy of Computer Science, but it does not appear to be just like the average philosophy of science or philosophy of engineering kind of stuff. Philosophers of computer science are still figuring out what exactly is computer science—such as “the meta-activity that is associated with programming”—but then finally settle for a weak “in the end, computer science is what computer scientists do”. Currently, the philosophy of computer science (PCS) is mostly an amalgamation of analyses of artefacts that are the products of doing computer science and many, many, research questions.
The comprehensive introductory overview of PCS in the Stanford Encyclopedia of Philosophy by Turner and Eden  starts with “some central issues” that are phrased into 27 principal questions that are in need of an answer. To name just a few: What kind of things are computer programs? What kind of things are digital objects, and do we need a new ontological category for them? What does it mean for a program to be correct? What is information? Why are there so many programming languages and programming paradigms? The remainder of the SEP entry on PCS is devoted to giving the setting of the discourses in some detail.
The contents in the entry focuses primarily on the dual nature of programs, programming languages, semantics, logic, proofs, and closes with legal and ethical issues in PCS; a selection that might be open to criticism by people who feel their pet topic ought to have been covered as well (but I leave it to them to stand up). The final words, however, are devoted to the nagging thought if PCS merely gives a twist to other fields of philosophy or if there are indeed new issues to resolve.
In any case, it is already noteworthy to read that Turner and Eden do not consider the act of programming itself as being part of computer science; and rightly so. That could be useful to take into account by people who write job openings offering new postdoc/assistant professor positions, many of which require “strong programming skills”. By the philosophers’ take on CS, they should have asked for good programmers but not researchers, because CS researchers are specialised in the meta-activities such as “design, development and investigation of the concepts and methodologies that facilitate and aid the specification, development, implementation and analysis of computational systems”  (emphasis added), i.e., not the actual development and implementation of software systems. On the other hand, the weird thing with the PCS entry is their CS-is-what-computer-scientists-do: if computer scientists decide to slack collectively, then PCS itself would degrade to investigate the non-output of CS, i.e., be obsolete, or, if research funding agencies were to pay mainly or only for ‘integrated projects’ that apply theory to develop working information systems for industry (or biologists, healthcare professionals, etc.), then that is what CS degenerates into? If that were the case, then CS would not merit to be called a science.
In this narrative, now would be a good place for a treatise on definitions of computer science to demonstrate the discipline is sane and structured, to simplify communication with non-informaticians, and feed philosophers with the settled basics to dwell upon. But then I would have to go into finer distinctions, made in e.g. the Netherlands, between informatika and informatiekunde (roughly, computer science vs. information engineering)—the former being more theoretical along the lines of the topics in the PCS entry and the latter includes more socio- psycho- cognitive- managerial topics—and extant definitions by the various organisations, dictionaries and so forth (e.g., here, here, here). I will do a bit more homework on this first, before writing anything about that (and before that, I will go to Geomatica’09 in Cuba and glue a few days holiday to the conference visit; so, within a few days, it will be quiet here until the end of February).
 Turner, R. and Eden, A. The Philosophy of Computer Science. In: Stanford Encyclopedia of Philosophy, Zalta, E. (Ed.), published 12 Dec. 2008.