A beginning note: does your repo really need to be pulled as root? Why? It's probably not a good idea to be doing that.
Github supplies https pull links that anyone can use to pull without needing a key. So, we can add another remote, used specifically for this purpose, that pulls using the https link.
git remote add autopull https://github.com/<user>/<repo>.git
Now you can change your pull command to:
git pull autopull master
From there, you can put it in .profile, .bash_profile, .bashrc, or maybe even a cron script. You haven't specified how you want to automate it, though, so I can't give any specific examples.
It should be noted that this can only work for public repositories. If this is a private repository, you should create another keypair that has no passphrase required. If it isn't your default keypair you can make use of a trick.
ssh-agent bash -c 'ssh-add /path/to/yourkey; git pull autopull master'
Or another answer to the same question:
GIT_SSH_COMMAND='ssh -i /path/to/yourkey' git pull autopull master