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La API de Google para acortar URLs permite acortar URLs, recuperar info del link original y las URLs acortadas de un usuario, aunque para usarlo se necesita crear una clave y dar de alta proyecto.

El resto es fácil, acceso mediante CURL y listo:

    define('GOOGLE_API_KEY', '[insert your key here]');
    define('GOOGLE_ENDPOINT', 'https://www.googleapis.com/urlshortener/v1');
 
    function shortenUrl($longUrl)
    {
        // initialize the cURL connection
        $ch = curl_init(
            sprintf('%s/url?key=%s', GOOGLE_ENDPOINT, GOOGLE_API_KEY)
        );
 
        // tell cURL to return the data rather than outputting it
        curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
 
        // create the data to be encoded into JSON
        $requestData = array(
            'longUrl' => $longUrl
        );
 
        // change the request type to POST
        curl_setopt($ch, CURLOPT_POST, true);
 
        // set the form content type for JSON data
        curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-type: application/json'));
 
        // set the post body to encoded JSON data
        curl_setopt($ch, CURLOPT_POSTFIELDS, json_encode($requestData));
 
        // perform the request
        $result = curl_exec($ch);
        curl_close($ch);
 
        // decode and return the JSON response
        return json_decode($result, true);
    }
 
    $response = shortenUrl('http://phpriot.com');
 
    echo sprintf(
        '%s was shortened to %s',
        $response['longUrl'],
        $response['id']
    );

Shortening URLs for goo.gl with Google’s URL Shortener API

Vía / PHPDeveloper.org