Fork spacewalkproject/spacewalk into your account.

Go to https://github.com/<youraccount>/spacewalk/wiki and click Create the first page and initialize wiki repository with some content.

Clone your forked spacewalk-wiki repository to your workstation.

 $ git clone git@github.com:<youraccount>/spacewalk-wiki.git

Go to the spacewalk-wiki repository and add a remote called wiki pointing to the spacewalk.wiki repository.

 $ cd spacewalk-wiki
 $ git remote add wiki git@github.com:<youraccount>/spacewalk.wiki.git

Make some new changes in test branch.

 $ git checkout -b test
 ...
 $ git commit

Publish test branch changes to spacewalk.wiki repository.

 $ git push -f wiki test:master

Check your changes on web - https://github.com/<youraccount>/spacewalk/wiki.

Now you can even edit wiki pages using GitHub web UI and then pull changes back to your working copy.

 $ git pull wiki master

When you are happy with changes in your working copy, publish these changes to forked spacewalk-wiki repository and open PR from test branch.

 $ git push -f origin test:test