class.xform.iw_recaptcha.inc.php

<?php
class rex_xform_iw_recaptcha extends rex_xform_abstract
{
    function enterObject()
    {
        $output = '<script src="https://www.google.com/recaptcha/api.js" async defer></script>';
        $output .= '<div class="g-recaptcha" data-sitekey="'.$this->getElement(1).'"></div>';
        $this->params['form_output'][$this->getId()] = $output;
    }

    function getDescription()
    {
        return 'iw_recaptcha -> iw_recaptcha|site_key';
    }
}
?>

class.xform.validate_iw_recaptcha.inc.php

<?php
class rex_xform_validate_iw_recaptcha extends rex_xform_validate_abstract
{

    function enterObject()
    {
        if ($this->params["send"] == "1")
        {
            if (isset($_POST['g-recaptcha-response']) && !empty($_POST['g-recaptcha-response']))
            {
                $secret = $this->getElement(2);
                $verifyResponse = file_get_contents('https://www.google.com/recaptcha/api/siteverify?secret=' . $secret . '&response=' . $_POST['g-recaptcha-response']);
                $responseData = json_decode($verifyResponse);
                if (!$responseData->success)
                {
                    $this->params["form_show"] = TRUE;
                    $this->params["hasWarnings"] = TRUE;
                    $this->params["warning_messages"][] = $this->getElement(3);
                }
            }
            else
            {
                $this->params["form_show"] = TRUE;
                $this->params["hasWarnings"] = TRUE;
                $this->params["warning_messages"][] = $this->getElement(4);
            }
        }
    }

    function getDescription()
    {
        return "validate|iw_recaptcha|secret_key|recaptcha_wrong|recaptcha_empty";
    }
}

?>