<?php   $my_user = new WP_User(get_current_user_id());  ?>
<form name="loginform" id="loginform" action="http://myreg_test_wordpress.loc/wp-content/themes/twentysixteen/my_auth.php" method="post">
    <div class="form-title "><h2>Authorization Form:</h2></div>
    <label>Email: <br />
        <input type="text" name="log" id="user_login" /></label>
    <label>Password :<br />
        <input type="password" name="pwd" id="user_pass" /></label>
    <label><input name="rememberme" type="checkbox" id="rememberme" value="forever" /> Запомнить меня</label>
    <input type="submit" name="wp-submit" id="wp-submit" value="Войти" />

    <input type="hidden" name="redirect_to" value="<?php bloginfo('url') ?>/my-temp-page-edit/" />
    <input type="hidden" name="testcookie" value="1" />
    <a href="<?php echo bloginfo('url').'/my-temp-page/' ?>"><div class="my_btn">Перейти на страницу регистрации</div></a>
</form>

$_SERVER['HTTP_REFERER'];
require_once( dirname(__FILE__) . '/../../../wp-load.php' );

if( is_user_logged_in() ) exit;

$my_user = new WP_User(get_current_user_id());

$credentials = array();
$credentials['user_login'] = $_POST['log'];
$credentials['user_password'] = $_POST['pwd'];
$credentials['remember'] = true;

// авторизуем
$user = wp_signon( $credentials, false );

// в случае неуспешной авторизации, смотрим, что не так
if ( is_wp_error($user) ) {
    echo $user->get_error_message();
}
echo'<pre>';var_dump($_POST);echo'</pre>';