You can use the get_avatar built-in function to get your gravatar as a favicon on your WordPress blog. For more detail read the below reference links. If your WordPress blog admin email and gravatar email is the same, you can add this simple line of code in your theme’s header.php file in the <head> section.
<link rel="shortcut icon" href="<?php echo get_avatar( get_option( 'admin_email' ), '16' ); ?> " />
Reference:
- http://codex.wordpress.org/Function_Reference/get_avatar
- http://codex.wordpress.org/Function_Reference/get_option
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