I just stared a new job and my boss does not post a schedule, she will just call me and tell me to come to work and if I don't she threatens to fire me.
What are the rules on posting a schedule.

What are the rules on posting a schedule. There are none.

While I think not advising employees of their work schedule is a poor way to run a business, there is no requirement that an employer does so. If your boss wants to call you at the last minute and tell you to come to work and threaten to fire you if you don't, she may.

If I were you, I'd be looking for a new job.