You can use author_link
filter to change the author’s link
add_filter( 'author_link', 'wpse110967_author_link', 10,2 );
function wpse110967_author_link( $link, $user_id ){
//Retrieve authors url from user meta
$_link = esc_url( get_user_meta( $user_id, 'wpse110967_author_link', true ) );
if( $_link )
$link = $_link;
return $link;
}
In the above example its assumed that you’ve stored the author-specified url as user meta with the key wpse110967_author_link
. If no url is found, it fallback to the default WordPress url.