How to create a polygon with right angled corners in Eagle?
You can't.

I don't like writing such short answers, but that's really all there is to say, you can't. Make the width something like 6mil (or whatever you minimum width DRC setting is) and then work with it. 6mil is tiny so you probably won't even notice it is rounded once manufactured, and unless you have some absolutely critical need for a perfect angle, then there are more important things in the design process to worry about.

Alternative Answer
Based on your update, there may be a way to do it.
You will need to be using the rectangle tool. Draw a series of boxes of the correct size, overlapping so that they form the shape you want. However these rectangles cannot belong to a signal/net. In order to connect it, you will have to draw a wire which goes up to the antenna and overlaps into it.
The overlapping rectangles shouldn't cause DRC errors where they overlap, but will give you a DRC error at the point where your signal wire intersects it. You'll just have to ignore this error.
What I am not 100% sure on is what Eagle does with rectangles in gerbers. For many things (including arcs with a cap set to flat), the Eagle CAM processor converts everything into lines. I presume this also applies to rectangles (haven't tried). If this is the case, the rectangles will end up with rounded corners anyway and so the result will be no different from using a 6mil polygon.

I did a quick google search, but couldn't find anything definitive on whether or not having a 3mil radius curve on all the corners of the antenna will make any difference (its only 0.07mm radius). However, I was looking at images of Bluetooth modules and many of them do in fact have noticeable rounded corners on the antenna line, like the example below. Granted in that example the curving is very pronounced - much larger than you would get from a 6mil polygon. On most of the pictures the rounded corners are much less obvious but definitely there.

Image Source