If you have the OAuth PHP library installed, you don't have to worry about forming the request yourself.
$oauth = new OAuth($consumer_key, $consumer_secret, OAUTH_SIG_METHOD_HMACSHA1, OAUTH_AUTH_TYPE_URI);
$oauth->setToken($access_token, $access_secret);
$oauth->fetch("https://api.twitter.com/1.1/statuses/user_timeline.json");
$twitter_data = json_decode($oauth->getLastResponse());
print_r($twitter_data);
For more information, check out The docs or their example. You can use pecl install oauth
to get the library.