Phil gave an excellent, accurate answer. Both are correct with a slight difference in meaning. English has many ways to describe an action or state in the future. Here is a useful overview: https://www.ef.com/ca/english-resources/english-grammar/future/ For a fuller version of Phil's explanation, see English Grammar in Use by Murphy, unit 19.

They are both correct, but the meanings are slightly different. The present simple makes reference to a schedule, timetable, or calendar — it basically means, “are you scheduled to work today?”. The present continuous, on the other hand, is a very common way of referring to future plans that are certain (or almost certain) to be realized in the (usually near) future.

"Are you working today?" is correct. We use the present continuous to talk about temporary actions, or actions happening at this moment in time. You could also ask "Are you working now?" and "Are you working this week?". "Do you work?" uses the present simple. We use the present simple to talk about actions which are usually true/always true.

While most people will tell you that either the second option is correct, or that both are possible, with variations in meaning, I do not think that is a good enough answer to you. In reality, most contexts of raising this sort of question occur in circumstances whereby the speaker is asking about the work schedule of the person in question, not about the process of working itself. Now, with timetables and schedules we rarely, if ever, use the Present Continuous. Use a "train" analogy: "Does this train leave at 5 PM today"? You would never, ever, say "Is this train leaving at 5 PM today" when asking about the departure timetable. The same applies here: "Are you scheduled to work today?" (I assume you are at work if so scheduled). In reality, most people would ask "Are you at work today" or "Do you work today" - because, most probably, the speaker is inquiring about availability of the person in question for today - not whether that person is actually doing any kind of work (for that matter, the person may have work today, but may not be doing it after all anyway).

Second one!