Well, APRSDroid is an Android app. It would probably be too much work getting it to run on Arduino, if it's even possible (my guess is it's not).
If you're a tinkerer, I would create a simple zero-crossing detector (with some hysteresis) and feed that to the Arduino. Then your code will just deal with decoding. I've done that (not with Arduino, but PIC). Decoding is pretty straightforward.