You have to surround the CSS with a <style>
tag:
<?php include 'header.php'; ?>
<style>
<?php include "https://stackoverflow.com/questions/6315772/CSS/main.css"; ?>
</style>
...
PHP include
works fine with .css
ending too. In this way you can even use PHP in your CSS file. That can be really helpful to organize e.g. colors as variables.