To add voice calls to a Yii2 PHP app, developers can use Twilio Programmable Voice. The process involves setting up a Yii2 basic application, installing the Twilio PHP SDK, and creating endpoints for TwiML, which is Twilio's Markup Language for building SMS and voice applications. For outbound calls, an example endpoint is created to notify a restaurant of an order, while for incoming calls, an endpoint is created to handle user inputs and process orders. The application can also make outgoing calls using the Twilio PHP SDK. To receive incoming calls, developers need to set up a webhook and enable receiving POST data from external sources, which allows the app to receive and process the call.