You sure can. Here’s a plugin that makes it possible throught the WP admin:
https://www.semiologic.com/software/static-front/
If your comfortable at writing html you can manually make the page (index.php in the your theme’s folder) static by taking out “the loop” (the WP script that displays your posts) and replacing it with static content. This is not advisised if your new to hand coding web pages. Also, you will not have access to this page throught the WP admin.
Actually, now that I think about it, it would be available through the WP admin. You could edit it through the “Files” tab in the menu.
