We have created a fully featured WooCommerce SMS extension. This plugin works for Australia, New Zealand, Singapore, UK and USA and does not require numbers to be in a specific format for delivery.
It is simple to install and is compatible with the latest versions of WordPress and WooCommerce.
Once you upload the extension you can access the settings from the WooCommerce Settings menu under the integration tab.
To install, download the plugin and upload via the Wordpress Plugins/Add New/Upload Plugin page.