  We present spatially and spectrally resolved Atacama Large
Millimeter/submillimeter Array (ALMA) observations of gas and dust in the disk
orbiting the pre-main sequence binary AK Sco. By forward-modeling the disk
velocity field traced by CO J=2-1 line emission, we infer the mass of the
central binary, $M_\ast = 2.49 \pm 0.10~M_\odot$, a new dynamical measurement
that is independent of stellar evolutionary models. Assuming the disk and
binary are co-planar within $\sim$2{\deg}, this disk-based binary mass
measurement is in excellent agreement with constraints from radial velocity
monitoring of the combined stellar spectra. These ALMA results are also
compared with the standard approach of estimating masses from the location of
the binary in the Hertzsprung-Russell diagram, using several common pre-main
sequence model grids. These models predict stellar masses that are marginally
consistent with our dynamical measurement (at $\sim 2\,\sigma$), but are
systematically high (by $\sim$10%). These same models consistently predict an
age of $18\pm1$ Myr for AK Sco, in line with its membership in the Upper
Centaurus-Lupus association but surprisingly old for it to still host a
gas-rich disk. As ALMA accumulates comparable data for large samples of
pre-main sequence stars, the methodology employed here to extract a dynamical
mass from the disk rotation curve should prove extraordinarily useful for
efforts to characterize the fundamental parameters of early stellar evolution.
