Simply Write New Post set type to ‘Link’. Or are you wanting to automate this?
It sounds like you’re using a custom WordPress theme. If so, do you have a link to the theme, or the site in question?
You can always include the old:
<a href="#" onclick="window.print();return false;">Print this page</a> in your page where you desire to include a print button. You can use a print button rather than text link if you prefer.