Can I inject a service into a directive in AngularJS?

You can do injection on Directives, and it looks just like it does everywhere else.

app.directive('changeIt', ['myData', function(myData){
    return {
        restrict: 'C',
        link: function (scope, element, attrs) {
            scope.name = myData.name;
        }
    }
 }]);

Change your directive definition from app.module to app.directive. Apart from that everything looks fine. Btw, very rarely do you have to inject a service into a directive. If you are injecting a service ( which usually is a data source or model ) into your directive ( which is kind of part of a view ), you are creating a direct coupling between your view and model. You need to separate them out by wiring them together using a controller.

It does work fine. I am not sure what you are doing which is wrong. Here is a plunk of it working.

http://plnkr.co/edit/M8omDEjvPvBtrBHM84Am