You can use the tutorial to install a Git server as aking1012 proposed you or you could just install SSH server on your EC2 instance (probably it would be wise to secure it and change the default port).
Git can be server-less you init your repository and then you access it from remote via SSH. So instructions like this on the Ubuntu Server should do it:
GIT_DIR=project.git git init
git --bare update-server-info
cp hooks/post-update.sample hooks/post-update
Finally install SSH on your server:
sudo apt-get install ssh-server
Now, you should configure SSH to secure it.
It's time to put your project online (the data you already have on your development machine):
git push ssh://<username>@<remote-git-hostname>/path/to/project.git master
And now you can start cloning around. You go on your development machine:
git clone ssh://<username>@<remote-git-hostname>/path/to/dir.git
Check this excellent resource on Git.
And for generating your ssh keys for safer authentication, you can read this article about SSH authentication.