Use beforeSend:

$.ajax({
         url: "http://localhost/PlatformPortal/Buyers/Account/SignIn",
         data: { signature: authHeader },
         type: "GET",
         beforeSend: function(xhr){xhr.setRequestHeader(‘X-Test-Header‘, ‘test-value‘);},
         success: function() { alert(‘Success!‘ + authHeader); }
      });

http://api.jquery.com/jQuery.ajax/

http://www.w3.org/TR/XMLHttpRequest/#the-setrequestheader-method