There isn't a way to do what you want easily, no. There is a way to do it, however, that is often used to publish things to servers and is used by some for GitHub Pages websites. It boils down to the following process:
git init git checkout --orphan deploy git add . git commit -m "Latest code" git remote add origin [repository-url] git push origin deploy --force
What this does is creates an "orphan" branch that is unrelated to the history of the rest of your repository. You then store the files that you want to deploy there, keeping them separate from your source code.
Let us know if you have more questions.