  We present Karl G. Jansky Very Large Array radio observations of the long
gamma-ray burst GRB 161219B ($z=0.147$) spanning $1-37$ GHz. The data exhibit
unusual behavior, including sharp spectral peaks and minutes-timescale
large-amplitude variability centered at $20$ GHz and spanning the full
frequency range. We attribute this behavior to scattering of the radio emission
by the turbulent ionized Galactic interstellar medium (ISM), including both
diffractive and refractive scintillation. However, the scintillation is much
stronger than predicted by a model of the Galactic electron density
distribution (NE2001); from the measured variability timescale and
decorrelation bandwidth we infer a scattering measure of $SM\approx
{(8-70)\times 10^{-4}}$ kpc m$^{-20/3}$ (up to ${25}$ times larger than
predicted in NE2001) and a scattering screen distance of $d_{\rm scr}\approx
{0.2-3}$ kpc. We infer an emission region size of $\theta_s \approx {0.9-4}$
$\mu$as ($\approx {(1-4)}\times 10^{16}$ cm) at $\approx4$ days, and find that
prior to 8 days the source size is an order of magnitude smaller than model
predictions for a uniformly illuminated disk or limb-brightened ring,
indicating a slightly off-axis viewing angle or significant substructure in the
emission region. Simultaneous multi-hour broadband radio observations of future
GRB afterglows will allow us to characterize the scintillation more completely,
and hence to probe the observer viewing angle, the evolution of the jet Lorentz
factor, the structure of the afterglow emission regions, and ISM turbulence at
high Galactic latitudes.
