function order_fields($fields) {

    $order = array(
        "billing_first_name",
        "billing_last_name",
        "billing_email",
        "billing_phone",
        "billing_country",
        "billing_address_1",
        "billing_address_2",
        "billing_city",
        "billing_state",
        "billing_postcode"
    );
    foreach ($order as $field) {
        $ordered_fields[$field] = $fields["billing"][$field];
    }

    $fields["billing"] = $ordered_fields;
    return $fields;
}

add_filter("woocommerce_checkout_fields", "order_fields");