Calculate phase shift between two signals
Do this procedure on both signals, and subtract the results to get what you want (it would be a nearly constant sequence whose value is phase shift in radians)


Perform FFT on the signal to obtain its spectrum.
Find the dominant harmonic of the signal : $f_c$ (where the peak of FFT occurs).
Filter the signal with a narrow-band linear phase filter (center = $f_c$, bandwidth as less as possible).
Again, perform FFT on the signal and extract its phase.


Note : It is assumed that the signal has a dominant frequency otherwise a phase shift is pointless