Many themes are created to simply display the author’s name using the username text by default instead of converting it to a link to the author’s website. We need to simple edit the code to make in order to display author website link in his post.
For that you need to edit the page.php or single.php file of your theme and search for this code:
<?php the_author() ?>
<?php the_author_link(); ?>
Now, it will automatically display a link to the author’s site which is specified in the users profile.