getjuicy

Woocommerce simple order notification allows you to receive a SMS when a new order is placed on your site. The plugin hooks into woocommerce and on order calls the twilio SMS service to send you a message with the order details.
You will need a twilio SID and auth token, plus a twilio number to use this plugin.
You can access the plugin options from the admin menu

Woocommerce-simple-order-notification

Woocommerce simple order notification allows you to receive a SMS when a new order is placed on your site.

DialBunny

DialBunny is a plugin that lets you make and receive calls and text messages through your Twilio account directly from your WordPress dashboard.

Woocommerce-simple-order-notification vs DialBunny