To do this on the server you would need to use one of the filters that ACF provides acf/load_field, acf/prepeare_field, or acf/load_value and the you would need to make a CURL or some other type of request to the API to get the result an populated to value.
On the client site you would need to use JavaScript to make the request using AJAX and use the ACF JavaScript API to populate the value.
