You might look into a magnetometer:

https://en.wikipedia.org/wiki/Magnetometer

https://www.adafruit.com/product/1120

Here's link to a video I made about using one to create an HTML5 animated compass:

https://www.youtube.com/watch?v=2YW6HWJg4f4

Here's a link to code I used and some install instructions for the Pi:

http://www.raspberryperl.com/compass/