Grant(s) for a Web Designer?

Well that is going to depend.  Web designers have been hired by organizations to design websites for the organizations (it's the organization that gets the grant and the grant money is used to pay the web designer).  There is one grant that comes to my mind that is for women to start an online business (depending upon if you are a woman).....

So obviously you are going to have to be a bit more specific.  In a word the answer to your question is "Yes" but it will depend on what kind of design.