Create a shell script with something like:
git pull origin master
You can store the file wherever you like.
Let's assume in /scripts/
Let's assume it's called getsite.sh
Make sure your file is executable:
chmod +x /scripts/getsite.sh
Run the command to make sure it works. I'll assume you've already run git init, and setup the repo.
Assuming it works OK, you can create a crontab entry to run it as often as you see fit:
You'll need an entry something along the lines of:
59 23 * * * /scripts/getsite.sh
This would run the script at 23:59 every day.
Read up on the man page for crontab if you need help with it.