how to set a facebook profile picture using the graph api

Upload the picture to an existing album (or create a new one) using the Graph API.
Will look something like this:

  $args = array('message' => 'Caption');
  $args['image'] = '@' . realpath("the_image.png");

  try {
    $data = $facebook->api("https://stackoverflow.com/".$album_uid.'/photos', 'post', $args);
  }
  catch(Exception $e) {
    print "<pre>";
    print_r($e);
    print "</pre>";
  }

Then get the uploaded image via the Graph API and redirect to the image’s link, add &makeprofile=1 to the querystring. The user will now be redirected to the profile image cropping page:

try {
  $pictue = $facebook->api("https://stackoverflow.com/".$data['id']);
  header("Location: ".$pictue['link']."&makeprofile=1");
}
catch(Exception $e) {
  print "<pre>";
  print_r($e);
  print "</pre>";
}