  The count rate of Weakly Interacting Massive Particle (WIMP) dark matter
candidates in direct detection experiments experiences an annual modulation due
to the Earth's motion around the Sun. In the standard isothermal halo model,
the signal peaks near June 2nd at high recoil energies; however, the signal
experiences a phase reversal and peaks in December at low energy recoils. We
show that this phase reversal may be used to determine the WIMP mass. If an
annual modulation were observed with the usual phase ({\it i.e.}, peaking on
June 2nd) in the lowest accessible energy recoil bins of the DAMA, CDMS-II,
CRESST-II, EDELWEISS-II, GENIUS-TF, ZEPLIN-II, XENON, or ZEPLIN-IV detectors,
one could immediately place upper bounds on the WIMP mass of [103, 48, 6, 97,
10, 52, 29, 29] GeV, respectively. In addition, detectors with adequate energy
resolution and sufficiently low recoil energy thresholds may determine the
crossover recoil energy at which the phase reverses, thereby obtaining an
independent measurement of the WIMP mass. We study the capabilities of various
detectors, and find that CRESST-II, ZEPLIN-II, and GENIUS-TF should be able to
observe the phase reversal in a few years of runtime, and can thus determine
the mass of the WIMP if it is $\mathcal{O}(100$ GeV). Xenon based detectors
with 1000 kg (XENON and ZEPLIN-IV) and with energy recoil thresholds of a few
keV require 25 kg-yr exposure, which will be readily attained in upcoming
experiments.
