Like the comments on this question stated, there is far too little detail in your post and it is far too localized of a question for this forum, but here is a general idea of what a project of this nature would require:
You would need to utilize the GitHub API to dynamically pull new posts, as well as to enable modifying of the content and reposting back to GitHub.
You would also need to develop a plugin that handles the integration of a GitHub repo with the WordPress posts using the WordPress API.
In general, posts are stored in a database. You would need to override (or supplement) this behavior with support for pulling from a new source (GitHub).
All that said, this is a massive job for what seems like a very small payoff. If you don't mind me asking, why would you want to do this?