This tutorial from ComputersPh.com is for replacing the WordPress 2.7 favicon 
Follow the same direction on how to create a favicon by reading post “How to replace favicon of Joomla! 1.5″. It is the same way to create a favicon.ico file.
In this tutorial, I will only show you where to upload the same file on to your WordPress website. We will be working with WordPress header.php file to locate the current favicon file location .
Once you have your new websites favicon, log on to your WordPress Admin panel then click (Appearance -> Editor -> header.php) with the Theme Editor. Locate this line in header.php file -> link rel=”Shortcut Icon” href=”?php echo get_settings(‘home’); /wp-content/themes/YourWPThemeFolder/images/favicon.ico” type=”image/x-icon” /.
Your new icon should go to folder (information taken from header.php)
/wp-content/themes/YourWPThemeFolder/images/.
Upload your file to the same website directory using FTP client then replace the existing favicon.ico. Open your browser then go to your website, you should now be able to see your new Favicon on your browser. For Internet Explorer, allow time for the favicon to appear.
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