Currently using this, but file that is stored is empty, so I supose no data is going through.
$post = array("file"=>'@'.$_FILES['uploadfile']['tmp_name']);
$ch = curl_init();
curl_setopt($ch,CURLOPT_HTTPHEADER,array('X-Parse-Application-Id : XXXXXXXXXXXXXX','X-Parse-REST-API-Key: XXXXXXXXx', 'Content-type: image/jpeg'));
curl_setopt($ch, CURLOPT_URL, 'https://api.parse.com/1/files/'.$_FILES['uploadfile']['name']);
curl_setopt($ch, CURLOPT_POST,1);
curl_setopt($ch, CURLOPT_BINARYTRANSFER, 1);
curl_setopt($ch, CURLOPT_POSTFIELDS, json_encode($post));
$result=curl_exec ($ch);
curl_close ($ch);
echo $result;