Git can work like this without other software. There are three protocol options you can use, according to Pro Git :
In your case, the Git protocol may be the most reasonable, because it is part of git, and so does not require other software.
The Git protocol is a special daemon, which is incorporated with Git. Listen for a dedicated port (9418), and give us a service similar to that of the SSH protocol; but without any authentication.
If you want authentication, you can consider using SSH.
The chapter Git on a server , from the Pro book Git , explains how to install git to use the git protocol, and SSH.
It is important to understand that this only serves as a server for Git; does not include the web interface like GitHub. Therefore, there are several options, such as GitLab , GitHub Enterprise , and others. There are also options with simpler web interfaces, such as GitWeb , which you can use in conjunction with your server. Git. But I can not make a specific recommendation for these, because the best option for you depends a lot on your case, your budget, and your preferences.