How to upload a folder (javascript app) to WordPress?

I should put it at:
wp-content/uploads/app

But wherever you put it, you will need to do more work to be able to see it live on your site.

You should make a child theme:
http://codex.wordpress.org/Child_Themes

Next, use a code snippet in functions.php for the child theme to load the javascript into the required page. Something like:

<?php
  add_action( 'wp_enqueue_scripts', 'add_my_script' );
  function add_my_script() {
    $my_page_id = 57; // set to the required page
    if ($my_page_id == get_the_id() ) {
      wp_enqueue_script( 'my-js', '/wp-content/uploads/app/whatever.js', array(), "1", true);
    }
  }

Other steps may be necessary depending on exactly how the app has been setup.