I’m not sure if it’s what you want, but I got some hints from How to display WordPress User Registration Form in front-end of the website? and Quick Tip: Making a Fancy WordPress Register Form from Scratch from Tutplus:
<?php
//add this to use wordpress functions outside wordpress
define( 'WP_USE_THEMES', false );
require('wp-blog-header.php');
?>
<html>
<head></head>
<body>
<div id="register-form">
<div class="title">
<h1>Register your Account</h1>
<span>Sign Up with us and Enjoy!</span>
</div>
<form action="<?php echo site_url('wp-login.php?action=register', 'login_post') ?>" method="post">
<input type="text" name="user_login" value="Username" id="user_login" class="input" />
<input type="text" name="user_email" value="E-Mail" id="user_email" class="input" />
<?php do_action('register_form'); ?>
<input type="submit" value="Register" id="register" />
</form>
</div>
</body>
</html>