This one is the last photo that the Mars rover took this week:
Why is the picture shown tilted? Why doesn't NASA rotate it and show it in the correct angle?
That's a picture of the remote sensing mast, which houses the main cameras. Since there's no one else there to be snapping the portrait, this had to be taken with one of the other cameras. In fact, it was taken from the Mars Hand Lens Imager camera on the robotic arm, and that's probably just the position it was in for the self-portrait, either because that's where there's a shot with no obstructions, or because it wasn't considered worth making extra moves.
If you watch this video, you can get some idea of the contortions the arm can make. The main point of the MAHLI camera is taking photos of the ground; the landscape scenery shots (and doubly-so the self portrait) is just bonus.
I'm guessing that the tilt is a combination of getting a clear shot plus reducing unnecessary movements. However, it's interesting to note that the same 30° tilt is there in the first color image from the surface, and NASA notes that this is the tilt in the stowed position. They're just in the process of putting the arm through its paces and maybe they hadn't gotten to the point of tilting the camera in a different way.
In any case, the image is presented rotated, to make the horizon align and to make down be down — in other words, they did "rotate it and show it in the correct angle". They could show the horizon tipped and the frame square, but why?
Direct answer to direct question, why did they not rotate it?
Because it would have looked like this:
Cropped from the already rotated image:
Rotating while keeping the horizontal rectangular shape means the photo will be cropped from corners. In a case of this much rotation the cropping is quite severe. So they chose to show all the image data they got, instead of cutting more than half of it away.