  We report the sky-projected orbital obliquity (spin-orbit angle) of WASP-84b,
a 0.70-$M_{\rm Jup}$ planet in a 8.52-day orbit around a G9V/K0V star, to be
$\lambda = 0.3 \pm 1.7^\circ$. We obtain a true obliquity of $\psi = 14.8 \pm
8.0^\circ$ from a measurement of the inclination of the stellar spin axis with
respect to the sky plane. Due to the young age and the weak tidal forcing of
the system, we suggest that the orbit of WASP-84b is unlikely to have both
realigned and circularised from the misaligned and/or eccentric orbit likely to
have arisen from high-eccentricity migration. Therefore we conclude that the
planet probably migrated via interaction with the protoplanetary disc. This
would make it the first short-orbit, giant planet to have been shown to have
migrated via this pathway. Further, we argue that the distribution of
obliquities for planets orbiting cool stars ($T_{\rm eff}$ < 6250 K) suggests
that high-eccentricity migration is an important pathway for the formation of
short-orbit, giant planets.
