How to let users choose posts order in categories?

First in your category.php (depending on your theme files) add a simple form to let the user sort A-Z or Z-A:

<form action="" name="custom_order" method="POST">
    <p> sort order:   
        <select name="CU_Order" id="CU_Order">
            <option value="ASC">A-Z</option>
            <option value="DESC">Z-A</option>
        </select>
    </p>
    <p> 
        <input type="hidden" name="cs_action" value="custom_sort_order">
        <input type="submit" name="submit" value="sort">
    </p>
</form>

then using pre_get_posts hook you alter the query to order like the user has selected:

add_action( 'pre_get_posts', 'change_sort_order' ); 
function change_sort_order(&$query){
    if (isset($_POST['cs_action']) && $_POST['cs_action'] == 'custom_sort_order'){
        global $wp;
        if (isset($wp->query_vars["CU_Order"])){
            $query->set( 'order', $wp->query_vars["CU_Order"] );
        }
    }
}

and all that is left is to add CU_Order order to the list of query vars WordPress knows using query_vars hook:

add_filter('query_vars', 'add_custom_order_query_vars');
function add_custom_order_query_vars($vars) {
    // add CU_Order to the valid list of variables
    $new_vars = array('CU_Order');
    $vars = $new_vars + $vars;
    return $vars;
}

simpler explanation:

• copy the first code in your
  category.php

• copy the rest in to your theme’s functions.php

• Done.