The update is not available from the Google Play Store, which means that you must get the apk from WhatsApp. You can find it at the sourcelink. The 18.52MB file requires Android 2.1 or higher. However, to get the calling feature, you need to be running Android 4.4 or higher.
Another Reddit user, Tropiux, has revealed how to use the feature without getting an invite. "Go to terminal...insert this command with root privileges...am start -n com.whatsapp/com.whatsapp.HomeActivity." You will have to do this every time you want to make a call. Once you are enabled, call someone with the latest version of the app. That will enable his WhatsApp calling feature, and once he calls you, your app will be permanently enabled.
Eventually, the Google Play Store should have the version of WhatsApp "in stock" with the voice call capability.
Screenshots showing the new WhatsApp UI with voice call feature
Thanks for the tip!
source: WhatsApp (APKMirror), Reddit (1), (2) via Amongtech