Oscilloscope

My scope allows me to set markers and it does the rest. Your scope may have a ruled grid on the screen that you can read how distant the shifted waves are. Knowing the time per divisions setting, you can easily calculate the phase shift.

Connect each signal to an input of a dual trace scope. Set the trigger on one of the inputs. Adjust the vertical positions of each trace to make identification of each waveforms zero crossing points. Count the number of horizontal divisions between each zero crossing and multiply by the sweep rate seconds per division. Its best to use the fastest sweep rate to stretch the waveforms out as much as possible for the highest resolution.