こんな感じ
<?php
$url = "https://qiita.com/api/v1/auth";
$data = array(
'url_name' => $url_name,
'password' => $password
);
$content = http_build_query($data);
$options = array('http' => array(
'method' => 'POST',
'content' => $content
));
$contents = file_get_contents($url, false, stream_context_create($options));
print($contents);
?>
