Chrome Extension communicate with rest web service

The API you're looking for is called XMLHttpRequest (also known as "AJAX"). Read the documentation at https://developer.chrome.com/extensions/xhr for more information.

Here's an example:

chrome.browserAction.onClicked.addListener(function(tab) { 
    var link = tab.url;
    var x = new XMLHttpRequest();
    x.open('GET', 'http://example.com/?whatever=' + link);
    x.onload = function() {
        alert(x.responseText);
    };
    x.send();
});

Note. The XMLHttpRequest API is asynchronous. This means that you cannot do something like this:

...
var result;
x.onload = function() {
    result = x.responseText;
};
x.send();
alert(result); // Does not behave as you expect!