  Rashba nanowires in a magnetic field exhibit a helical regime when the
spin-orbit momentum is close to the Fermi momentum, k_F \approx k_{SO}. We show
that this regime is characterized by a strongly anisotropic electron spin
susceptibility, with an exponentially suppressed signal along one direction in
spin space, and that there are no low frequency spin fluctuations along this
direction. Since the spin response in the gapless regime k_F \not \approx
k_{SO} has a power law behavior in all three directions, spin measurements
provide a signature of the helical regime that complements spin-insensitive
conductance measurements.
