angular-datepicker.html

<script type="text/javascript" src="js/bootstrap-datepicker.js"></script>
<div id="datepicker"></div>

<script type="text/javascript">
        $('#datepicker').datepicker().on('changeDate', function(ev){
          var element = angular.element($('#datepicker'));
          var controller = element.controller();
          var scope = element.scope();

          scope.$apply(function(){
            scope.doSomethingWithDate(ev.date);
          });
        });
</script>

And then in your controller.js:

<script type="text/javascript">
$scope.doSomethingWithDate = function (date){
  alert(date);
};
</script>