My Account shortcode:

[woocommerce_my_account order_count=”-1″]
Shows the ‘my account’ section where the customer can view past orders and update their information. You can specify the number or order to show, it’s set by default to 15 (use -1 to display all orders.)
Reference: Woocommerce Shortcodes

Only the orders
Roll your own shortcode:

function shortcode_my_orders( $atts ) {
    extract( shortcode_atts( array(
        'order_count' => -1
    ), $atts ) );

    wc_get_template( 'myaccount/my-orders.php', array(
        'current_user'  => get_user_by( 'id', get_current_user_id() ),
        'order_count'   => $order_count
    ) );
    return ob_get_clean();
add_shortcode('my_orders', 'shortcode_my_orders');

Add this in a plugin or to your functions.php file and then use it like [my_orders order_counts=10] (order_counts is optional, if missing it lists all the orders).