The phasor of a function (wave) containing variables other than time, in this case distance z, is I believe represented by a function including z but not t.
So the phasor of A cos(wt - kz) would be A exp(-jkz) as the time function is Re{A exp j(wt - kz)}. The exp(jwt) is left out of the phasor expression since in any equation using phasors that term cancels out. At least that's been my experience with e-m wave phasors.
So if the time function is A sin(wt - kz + θ), what do you think the phasor is?
Hint: change your time function to read A cos(wt - kz + ψ).