To play an audio file in a Twilio Video call, a participant needs to create an invisible `<audio>` element and load the desired audio file into it. The `captureStream()` method of the `<audio>` element is used to obtain a MediaStream object, which includes an audio track that can be published to the video room as a local audio track using the Twilio Video library's `LocalAudioTrack` class. Once the track is published, all participants in the call will receive the audio playback. The application must decide when to stop sharing audio and clean up by unpublishing the track when it ends or when the user stops playback. A fully working example of this technique can be implemented using Twilio Serverless and a Node.js version compatible with Twilio Functions.