Is there a site that can provide me a feed of scholarly works that cite another scholarly work as they are published?
Yes, this can be done in a number of ways:
In Google Scholar, you can set up an "alert" for citations of any paper that you're interested in. Scholar is very broad in its collection of data, so this will include citations not just in peer reviewed journal articles but also citations in ArXiv preprints, theses, conference proceedings papers, and all sorts of "grey literature." Google Scholar alerts are free.
In Thomson Reuter's "Web of Science", you can have saved searches that generate alerts that are emailed to you. In comparison with Google Scholar, Web of Science indexes a much smaller set of publications, so the coverage is not as broad. Furthermore, you (or your institution) need a subscription to the service.
Elsevier's Scopus database also offers alerts.