Yes, but you would have to turn your home.php file into a template file.
To do so, add this at the top of the home.php file, right under the <?php –
// Template Name: Home
Then create a page called “home” (you may have already done this). In the page editor, make sure and select the “Home” template on the right. Then you can go back to your settings and select the home page as your static page if you need to.