Do we have Graphic design career option here in stack exchange graphics, like we have in Stack overflow career?
At the moment there is only one careers.
However, and although the focus there is on stackoverflow, if you create a profile your reputation on GD.SE will also be displayed after the work experience area. You can also pick your best questions and answers from any SE site and place them at the bottom.
I've seen and applied for a few design positions through careers in the past, so I'd say: give it a try :)