$ch = curl_init('http://site.ru/handler');
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'PUT');
curl_setopt($ch, CURLOPT_POSTFIELDS, 'postdata');
curl_exec($ch);
curl_close();
Аналогично с DELETE
$ch = curl_init('http://site.ru/handler');
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'DELETE');
curl_exec($ch);
curl_close();