How can I add a PHP page to WordPress?

You don’t need to interact with the API or use a plugin.

First, duplicate post.php or page.php in your theme folder (under /wp-content/themes/themename/).

Rename the new file as templatename.php (where templatename is what you want to call your new template). To add your new template to the list of available templates, enter the following at the top of the new file:

<?php
/*
Template Name: Name of Template
*/
?>

You can modify this file (using PHP) to include other files or whatever you need.

Then create a new page in your WordPress blog, and in the page editing screen you’ll see a Template dropdown in the Attributes widget to the right. Select your new template and publish the page.

Your new page will use the PHP code defined in templatename.php

Source: Creating Custom Page Templates for Global Use