The recent discovery of a Gunn-Peterson (GP) trough in the spectrum of the redshift 6.28 SDSS quasar has raised the tantalizing possibility that we have detected the reionization of the universe. However, a neutral fraction (of hydrogen) as small as 0.1% is sufficient to cause the GP trough; hence, its detection alone cannot rule out reionization at a much earlier epoch. The cosmic microwave background (CMB) polarization anisotropy offers an alternative way to explore the dark age of the universe. We show that for most models constrained by the current CMB data and by the discovery of a GP trough (showing that reionization occurred atz > 6.3),Microwave Anisotropy Probe (MAP) can detect the reionization signature in the polarization power spectrum. The expected 1 σ error on the measurement of the electron optical depth is around 0.03 with a weak dependence on the value of that optical depth. Such a constraint on the optical depth will allowMAP to achieve a 1 σ error on the amplitude of the primordial power spectrum of 6%.MAP with 2 yr (Planck with 1 yr) of observation can distinguish a model with 50% (6%) partial ionization between redshifts of 6.3 and 20 from a model in which hydrogen was completely neutral at redshifts greater than 6.3.Planck will be able to distinguish between different reionization histories even when they imply the same optical depth to electron scattering for the CMB photons.