Wordpress - Displaying a custom post type alphabetically

try this:

<?php 
$args = array( 'post_type' => 'tenant', 'posts_per_page'=>5, 'orderby'=>'title','order'=>'ASC');
$loop = new WP_Query( $args );
while ( $loop->have_posts() ) : $loop->the_post();
?>

You will find more info o custom queries here: http://codex.wordpress.org/Class_Reference/WP_Query

I realize this is an old thread, but I came across it trying to do the same thing and settled on adding a pre-query action using functions.php rather than a template and the loop.

In my case; I have a page of about 25 yoga classes, set up as a custom post type 'classes'

// function and action to order classes alphabetically

function alpha_order_classes( $query ) {
    if ( $query->is_post_type_archive('classes') && $query->is_main_query() ) {
        $query->set( 'orderby', 'title' );
        $query->set( 'order', 'ASC' );
    }
}

add_action( 'pre_get_posts', 'alpha_order_classes' );