Ok this is my take on adding the recaptcha.
It is pure alpha, nothing tested, simply written by the instructions of 
ReCaptcha for PHP. All operations are done in /class/captcha/ and all needed things are in the link above.
-1- download the Recaptcha and extract recaptchalib.php
-2- register and obtain an API key
-3- modify config.php and fill in your private key
 return $config = array( 
    "disabled"              => false,                   // Disable CAPTCHA 
    "mode"                  => 'recaptcha',             // default mode  image, text or recaptcha 
    "name"                  => 'xoopscaptcha',          // captcha name 
    "skipmember"            => true,                    // Skip CAPTCHA check for members 
    "maxattempt"            => 10,                      // Maximum attempts for each session 
    "num_chars"             => 4,                       // Maximum characters 
    "rule_text"             => _CAPTCHA_RULE_TEXT, 
    "maxattempt_text"       => _CAPTCHA_MAXATTEMPTS, 
    "private_key"           => 'myAPIkey' 
    ); 
?>  
-4- add config.recaptcha.php and fill in your public key
  
return $config = array( 
    "public_key"           => 'myAPIkey' 
    ); 
?>  
-5- add recaptcha.php
  
class XoopsCaptchaRecaptcha extends XoopsCaptchaMethod 
{ 
 
     
    function __construct($handler = null) 
    { 
        parent::__construct($handler); 
        parent::loadConfig('recaptcha'); 
    } 
     
    function XoopsCaptchaImage($handler = null) 
    { 
        $this->__construct($handler); 
    } 
     
    function isActive() 
    { 
         
        return true; 
    } 
     
    function render() 
    { 
        $image = $this->loadImage(); 
        return $image . '
'; 
    } 
 
    function loadImage() 
    { 
        require_once(XOOPS_ROOT_PATH . '/class/captcha/'.'recaptchalib.php'); 
        $publickey = $this->config["public_key"]; // you got this from the signup page see config.captcha.php 
        $ret = recaptcha_get_html($publickey); 
        
        return $ret; 
    } 
} 
?>  
-6- insert 
 // Verify the ReCaptcha code 
        } elseif ($this->config["mode"] == 'recaptcha') { 
            require_once(XOOPS_ROOT_PATH . '/class/captcha/'.'recaptchalib.php'); 
            $privatekey = $this->config["private_key"] ; 
            $resp = recaptcha_check_answer ($privatekey, 
                                $_SERVER["REMOTE_ADDR"], 
                                $_POST["recaptcha_challenge_field"], 
                                $_POST["recaptcha_response_field"]); 
            if (!$resp->is_valid) { 
              $this->message[] = $resp->error; 
            } 
            else { 
              $is_valid = true; 
            } 
        // Verify the code Captcha  
before
 } elseif (!empty($_SESSION["{$sessionName}_code"])) { 
            $func = !empty($this->config["casesensitive"]) ? "strcmp" : "strcasecmp"; 
            $is_valid = ! $func( trim(@$_POST[$sessionName]), $_SESSION["{$sessionName}_code"] ); 
        }  
in xoopscaptcha.php
You need also to change:
 $this->path_plugin = XOOPS_ROOT_PATH . "/Frameworks/captcha";  
to
 $this->path_plugin = XOOPS_ROOT_PATH . '/class/captcha';  
in xoopscaptcha.php
-7- test
Edit: corrected include path and made it clearer for public and private keys.
- Added correction for Frameworks relic