How can I predict the direction and arc of an Arcane Sentry?

There IS now a way to see which way the sentry will start. No way to determine which way it will rotate, but you can at least make sure you're not standing in it's way when it starts. Take a look:

Here, you can see where the sentry is going to spear out. It's almost due north.

The closer it is to activating, the more pronounced the effect gets:

So now that you now where it's going to start, you can be that much safer before it activates and kills you instantly.

There is no way to predict it. The lasers are always the same length, however, so the best course of action is to accustom yourself to the length and get out of range before the laser appears. Short of that, it does start moving immediately after it is created, and it moves fairly slowly, so if you can't get completely away from the laser, at least move away from walls and corners so you have a freer range of motion to try to avoid the laser once it begins moving.

With all the classes, there are skills you can use that will drastically help you avoid the laser if you do get trapped in a bad place. Try to take advantage of movement skills to help the situation.