When you write and app with Icenium, it's almost exactly like writing a standard HTML5 web application. Therefore, if you are accessing a service layer like Web API, you can make a standard ajax call with jQuery's $.ajax like so:
$.ajax({
type: "get",
url: "http://somewhere.com/service",
contentType: "application/json",
dataType: "json",
success: function (x) {
console.log(x);
}
});