Although all of the answers above are good, I would like to propose a new method instead of using the symbolic link method in public html directory as proposed BEST in the accepted answer. You need to have access to your server virtual host configurations.
It is about configuring virtual host of your web server directly pointing to the repository directory. In Apache you can do it like:
DocumentRoot /var/www/html/website/your-git-repo
Here is an example of a virtual host file:
<VirtualHost *:443>
ServerName example.com
DocumentRoot /path/to/your-git-repo
...
...
...
...
</VirtualHost>