Here is the code. It still looks messed up even without the style I have here.
I think the problem is some other CSS that is being applied to the recaptcha but I don't really know how to figure out what to fix.
<div style="margin:0 auto;width:320px;">
<?php // Display reCaptcha
$path = plugin_dir_path( __FILE__ );
$publickey = "6LdFHtE22k7vXv93C";