I was talking to someone the other day about this. There are some tasks that AIs can do better than the average human and one of them is audio transcription. OpenAI Whisper is incredibly good at transcribing audio in multiple languages, even when the sound is pretty bad. It's really, really impressive. So it can already be used as a sort of "gig worker", where you give it the audio and it outputs the text (there are already a myriad of self-hosted solutions so you don't need to run the model yourself).

But if you're referring to the job in terms of everything it includes, things like working with your team, interacting with your boss, doing various real world tasks, we're not quite there yet. This might change in a year or two though. Also, some (perhaps an increasing amount of) jobs are reducible to gigs, so in those cases it's more clear cut.