WOW.js Script Tag Initialization Header/Footer

The theme should enqueue styles and scripts on the wp_enqueue_scripts hook, per Codex recommendations.

function theme_enqueue_scripts()
// register wow.js & animate.css
    wp_enqueue_style( 'animate-stylesheet', get_stylesheet_directory_uri() . '/library/css/animate.css', array(), '', 'all' );
    wp_enqueue_script( 'wow-js', get_stylesheet_directory_uri() . '/library/js/vendor/wow.min.js', array(), '', 'all' );
}
add_action('wp_enqueue_scripts', 'theme_enqueue_scripts' );

Then your initization script can be added to the wp_head hook.

function wpa_135542(){?>
<script>
 new WOW().init();
</script>
<?php }
add_action( 'wp_head', 'wpa_135542' );