gravatar_site_icon.php

<?php
/**
 * Use Gravatar as your site icon, add the code to your (child) theme functions.php or use it in a plugin
 * Requires: WordPress 4.3
 *
 * @param  array $meta_tags default site icon meta tags array
 * @return array            return the modified site icon meta tags array
 */
function gravatar_site_icon ($meta_tags) {

	$email = get_bloginfo('admin_email', 'raw'); // modify this if you want to use another email address, eg: $email = 'name@domain.com';
	$email_md5_hash = md5(strtolower(trim($email)));

	$meta_tags = array(
		sprintf( '<link rel="icon" href="%s" sizes="32x32" />', 'http://www.gravatar.com/avatar/' . $email_md5_hash . '?s=32;' ) ),
		sprintf( '<link rel="icon" href="%s" sizes="192x192" />', 'http://www.gravatar.com/avatar/' . $email_md5_hash . '?s=192;' ) ),
		sprintf( '<link rel="apple-touch-icon-precomposed" href="%s">', 'http://www.gravatar.com/avatar/' . $email_md5_hash . '?s=180;' ) ),
		sprintf( '<meta name="msapplication-TileImage" content="%s">', 'http://www.gravatar.com/avatar/' . $email_md5_hash . '?s=270;' ) ),
	);
	return $meta_tags;
}

add_filters( 'site_icon_meta_tags', 'gravatar_site_icon' );