Start with it [Elgg 1.8]:

$(document).ready(function(){
        $("button").click(function(){
            $.ajax({
                type: "GET",
                url: "http://localhost/elgg/services/api/rest/json/",
                data: "method=auth.gettoken",
                dataType: "json",
                success:function(result){
                    alert(result);
                }
            });
        });
    });

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Ok, but the method auth.gettoken requires the username and password... I want to call a service with the logged user.. without store the username and password.

I implemented a solution generating a token manually with the following code to use in future requests .. I do not know if it's the best way to do this but it worked..

/views/default/js/api_token.php

<?php
if(!elgg_is_logged_in()){
    exit;
}
$token = create_user_token(elgg_get_logged_in_user_entity()->username);
?>
define("SocialPRO/ClientApiToken", ['elgg'], function (elgg) {
    elgg.clientApiToken = '<?php echo $token;?>';
});

This doesn't seem right. Why are you using web services for a user that is already logged into Elgg? The whole point of web services is to allow integration with other software.

@Gustavo Caldeira What's your goal?

I'm creating an Angular page... and calling services from that..

https://community.elgg.org/discussion/view/2167945/why-not-allow-js-applications-calls-webservice-methods