Manually setup a git repo in /etc or take a look at the etckeeper package. Don’t use a public repository, /etc can expose sensitive data such as password hashes or private keys.

apt get install etckeeper git incrontab

nano /etc/etckeeper/etckeeper.conf , set VCS="git" (comment the other options) and set PUSH_REMOTE="origin".

# Go to the configuration directory.
cd /etc
# Initialize etckeeper.
etckeeper init
# Add the remote repository.
git remote add origin git@HOSTNAME:REPONAME
# First commit.
etckeeper commit "Initial commit."
# Set the upstream and push.
git push -u origin master

You can use https and username:password@HOSTNAME/REPONAME.GIT while adding origin to automatically do things on behalf on that user.

Now, let’s tell incrotab to trigger an automatic commit on every created, modificed or deleted folder or file in /etc :

# Edit incrotab jobs
incrontab -e 
# Add this line
/etc IN_MODIFY,IN_CREATE,IN_DELETE,IN_MOVED_TO etckeeper commit "incrontab trigger"