Is there a way to recover a carrier of an FM signal to use for an Angle of Arrival calculation?  I am using GNURadio and gr-aoa (https://github.com/MarcinWachowiak/gr-aoa) and I am trying to use the NOAA Weather Radio signals.

I'm not quite sure what you're trying to do, but you can recover the phase of an FM carrier at baseband by detecting the angle of the complex vector at baseband just like with any other signal.    If you are using multiple antennas and mix all of the inputs to baseband with the same reference, then the relative phases of each will be apparent and useful for comparison.