Grigory Klyushnikov, the former developer of VK Android app, published an open-source Android version of Clubhouse on GitHub. He reverse-engineered the Clubhouse API project. The following features work: login, seeing the list of rooms, joining rooms from said list and by direct links, listening, speaking and raising hand. Registration should work too, but Grigory suggests that users better use an iOS device to register.
Android users just need to download and install the APK file of the app. There is a warning: Clubhouse may ban accounts using unofficial Android app.
"This is more of a proof of concept, a stopgap measure before Clubhouse releases their official Android app that I'm sure they're making right now", Grigory says. You can download the APK file here.