recaptcha working on local but not on live wordpress sites [closed]

Tip A URL can be used as a filename with this function if the fopen
wrappers have been enabled. See fopen() for more details on how to
specify the filename. See the Supported Protocols and Wrappers for
links to information about what abilities the various wrappers have,
notes on their usage, and information on any predefined variables they
may provide.

So most probably allow_url_fopen is set to false on your server.

But you shouldn’t use that function – use wp_remote_get instead.