You can do this with javascript.
function request(){
var xhr = getXHR();
xhr.addEventListener("error", transferFailed, false);
xhr.addEventListener("abort", transferCanceled, false);
xhr.open("GET", baseURL+"/rest/api/2/issue/KEY-1", false);
xhr.setRequestHeader("Authorization", "Basic "+btoa("admin:admin"))
xhr.setRequestHeader('Content-Type', 'application/json');
xhr.send();
}
Ensure that it is synchronous and jira server conf has:
Header always set Access-Control-Allow-Credentials "true"
Header set Access-Control-Allow-Headers "Authorization, Origin, X-Requested-With, Content-Type, Accept"