How to order the posts by view count only for category pages

Try this…

Install the WP-PostViews plugin http://wordpress.org/extend/plugins/wp-postviews/

Then incorporate this code into your theme’s Category template:

<?php if (function_exists('get_most_viewed_category') && intval(get_query_var("cat")) > 0): ?>
<ul>
<?php get_most_viewed_category(get_query_var("cat"),'both',10); ?>
</ul>
<?php endif; ?>

according to this thread http://wordpress.org/support/topic/get-query?replies=8

When you view a category page you should see the posts within that category listed by most views in descending order.