We report the sky-projected orbital obliquity ( spin-orbit angle ) of WASP-84b , a 0.70- M _ { 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 _ { eff } < 6250 K ) suggests that high-eccentricity migration is an important pathway for the formation of short-orbit , giant planets .