Display Posts of a Category in Alphabetical Order (Custom Post Type)

Use the pre_get_posts action to modify the query before it is run. Place this in your theme’s functions.php:

function wpd_tax_alpha( $query ) {
    if ( $query->is_tax('link-category') && $query->is_main_query() ) {
        $query->set( 'orderby', 'title' );
        $query->set( 'order', 'ASC' );
    }
}
add_action( 'pre_get_posts', 'wpd_tax_alpha' );