The ability to cite software and give credit to its authors and contributors is increasingly important. While the number of online open-source software repositories has grown rapidly over the past few years, few are being properly cited when used due to the difficulty of creating appropriate citations and the lack of automated techniques. This paper presents GitCite, a model for software citation with version control which enables citations to be inferred for any project component based on a small number of explicit citations attached to subdirectories/files, and an implementation that integrates with Git and GitHub. The implementation includes a browser extension and a local executable tool, which enable citations to be added/modified/deleted to software project repositories and managed through functions such as fork/merge/copy.