  We measure the circular velocity curve $v_{\rm c}(R)$ of the Milky Way with
the highest precision to date across Galactocentric distances of $5\leq R \leq
25$ kpc. Our analysis draws on the $6$-dimensional phase-space coordinates of
$\gtrsim 23,000$ luminous red-giant stars, for which we previously determined
precise parallaxes using a data-driven model that combines spectral data from
APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the
circular velocity curve with the Jeans equation assuming an axisymmetric
gravitational potential. At the location of the Sun we determine the circular
velocity with its formal uncertainty to be $v_{\rm c}(R_{\odot}) =
(229.0\pm0.2)\rm\,km\,s^{-1}$ with systematic uncertainties at the $\sim 2-5\%$
level. We find that the velocity curve is gently but significantly declining at
$(-1.7\pm0.1)\rm\,km\,s^{-1}\,kpc^{-1}$, with a systematic uncertainty of
$0.46\rm\,km\,s^{-1}\,kpc^{-1}$, beyond the inner $5$ kpc. We exclude the inner
$5$ kpc from our analysis due to the presence of the Galactic bar, which
strongly influences the kinematic structure and requires modeling in a
non-axisymmetric potential. Combining our results with external measurements of
the mass distribution for the baryonic components of the Milky Way from other
studies, we estimate the Galaxy's dark halo mass within the virial radius to be
$M_{\rm vir} = (7.25\pm0.26)\cdot 10^{11}M_{\odot}$ and a local dark matter
density of $\rho_{\rm dm}(R_{\odot}) = 0.30\pm0.03\,\rm GeV\,cm^{-3}$.
