  A number of radio interferometers are currently being planned or constructed
to observe 21 cm emission from reionization. Not only will such measurements
provide a detailed view of that epoch, but, since the 21 cm emission also
traces the distribution of matter in the Universe, this signal can be used to
constrain cosmological parameters at 6 < z < 20. The sensitivity of an
interferometer to the cosmological information in the signal may depend on how
precisely the angular dependence of the 21 cm 3-D power spectrum can be
measured. Utilizing an analytic model for reionization, we quantify all the
effects that break the spherical symmetry of the 3-D 21 cm power spectrum and
produce physically motivated predictions for this power spectrum. We find that
upcoming observatories will be sensitive to the 21 cm signal over a wide range
of scales, from larger than 100 to as small as 1 comoving Mpc. We consider
three methods to measure cosmological parameters from the signal: (1) direct
fitting of the density power spectrum to the signal, (2) using only the
velocity field fluctuations in the signal, (3) looking at the signal at large
enough scales such that all fluctuations trace the density field. With the
foremost method, the first generation of 21 cm observations should moderately
improve existing constraints on cosmological parameters for certain
low-redshift reionization scenarios, and a two year observation with the second
generation interferometer MWA5000 can improve constraints on Omega_w, Omega_m
h^2, Omega_b h^2, Omega_nu, n_s, and alpha_s. If the Universe is substantially
ionized by z = 12 or if spin temperature fluctuations are important, we show
that it will be difficult to place competitive constraints on cosmological
parameters with any of the considered methods.
