Well, there is no one good way to do this. However, here is a suggestion.
What you can do is create a bare repository on your server, outside the public directory. This repository will push changes to your SVN repository and will be like the gate keeper for your SVN repo. Your website already runs an SVN repository.
$ cd; mkdir site_bare.git; cd site_bare.git
$ git --bare init
You can use a shell script, something like https://github.com/deanc/wordpress-plugin-git-svn on the post-commit hook on this bare repository.
#!/bin/sh
echo
echo "**** Pulling changes into the SVN repository [Hub's post-update hook]"
echo
cd $HOME/www || exit
unset GIT_DIR
# Change to SVN dir and commit changes
echo "Changing directory to SVN and committing to trunk"
cd $SVNPATH/trunk
svn commit --username=$SVNUSER -m "$COMMITMSG"
# Create a new tag and commit it :)
echo "Creating new SVN tag"
cd $SVNPATH
svn copy trunk/ tags/$NEWVERSION1
svn commit --username=$SVNUSER -m "Updating tag to $NEWVERSION1"
# Update the version number
echo "Updating version number for future executions"
cd $CURRENTDIR
echo $NEWVERSION1 > version.txt
exec git-update-server-info
I have taken this from https://github.com/deanc/wordpress-plugin-git-svn/blob/master/deploy.sh but you can get the git commit message directly instead of asking for one.
On your local machine, add the bare repository as a remote and push changes to it:
git remote add bare <bare-repository-url>
How this works is, you write some code and push it to the bare repository, which using its post-update hook to push changes to the SVN repo.
You will have to modify the code above to push changes. I have just given a reference.
