Shiptheory can gather what3words addresses from Woocommerce. In order to do this follow what3word's installation instructions here

Once you have installed the plugin, Shiptheory will automatically download a what3words address if a customer includes it at checkout. For example:

The what3words address of ///fears.snake.rotate has been included in the optional field in our Woocommerce store's checkout. 

The address can be seen in the shipment popup from the dashboard after being pulled into Shiptheory.