Create a child theme for twenty ten, then copy across loop.php to the child theme, rename the copied file loop-category.php
Open the file and before these lines:
<?php /* If there are no posts to display, such as an empty archive page */ ?>
<?php if ( ! have_posts() ) : ?>
Add a line to reverse the sort order!
<?php query_posts($query_string . "&order=ASC"); ?>
So you have:
<?php /* Reverse the sort order ascending */ ?>
<?php query_posts($query_string . "&order=ASC"); ?>
<?php /* If there are no posts to display, such as an empty archive page */ ?>
<?php if ( ! have_posts() ) : ?>
Twenty Ten Child Theme:
If you want to make it better and category specific, or do not want to code it yourself, I have already posted about this and there is a child theme, I use it for a series of posts like, part 1, part 2 etc:
So if you have no other changes, job done!
Twenty Eleven Child Theme (Page of Posts):
This variation uses Custom Fields, and is a template page rather than index.pgp or category.php, and is for twenty eleven.
HTH
David