Q:

Does Github have a way to synchronize your fork with cloned repo? 

Does Github offer a way to synchronize a fork of a Github repo with changes in the source repo? 
For instance say I fork a repo, and rename the master to upstream which I want to keep synchronized with changes to the source repo, can Github synchronize my upstream with the master of the source repo regularly? 

A:

No, github does not provide it.  Instead you can achieve it locally. 
First, create local repository, add your own remote and retrieve it. 
git init
git remote add origin git@github.com:<username>/<repo>.git
git pull origin master

Next step, add a remote branch to your repository that points to the original repo you forked from. 
git remote add --track master <repo-name> git://github.com/<username>/<source-repo>.git

Note that master will be the branch you want to track in the forked repo.  <repo-name> is up to you.  If you want to verify, simply run git remote and you must see <repo-name> and origin as output. 
Now, you are ready to get all new changes from original repo. 
git fetch <repo-name>

A new branch called <repo-name>/master will be created with latest changes.