You can not delete style.css and have a functioning theme (at least without hacking WordPress core files). All the theme meta information is written in the style specifically. You can, however register another css file named my-style.css
or whatever the name you want.
function my_theme_css() {
wp_enqueue_style( 'my-style', get_template_directory() . '/my-style.css' );
}
add_action( 'wp_enqueue_scripts', 'my_theme_css' );
Now, your style.css does not have any css so you may want to remove it from your html. You can remove it from your site's <head>
using wp_dequeue_style(). But the physical file has to be there in your theme's directory.
add_action('init','_remove_style');
function _remove_style(){
wp_dequeue_style('style.css');
}