WP .js script file not loading

According to codex, get_stylesheet_directory_uri() does not including a trailing slash. So, you might want to use it in the following way:

function wpb_adding_scripts() {
  wp_register_script('my_scripts', get_stylesheet_directory_uri().'/js/scripts.js', array('jquery'),'1.1', true);
  wp_enqueue_script('my_scripts');
}
add_action( 'wp_enqueue_scripts', 'wpb_adding_scripts' );

UPDATE

If you want to use jQuery in your scripts, you should do it in one of these ways:

1. Use jQuery instead of $ to avoid conflict
2. Create a self invoking function and pass $ to it.

Take a look at this example:

(function($){
    $(document).ready(function(){
      alert("test");
    })
})(jQuery);