Stellar feedback plays a fundamental role in shaping the evolution of galaxies. Here we explore the use of ionised gas kinematics in young, bipolar H II regions as a probe of early feedback in these star-forming environments. We have undertaken a multiwavelength study of a young, bipolar H II region in the Galactic disc, G$316.81-0.06$, which lies at the centre of a massive ($sim10^3$ M$_{odot}$) infrared-dark cloud filament. It is still accreting molecular gas as well as driving a $sim 0.2$ pc ionised gas outflow perpendicular to the filament. Intriguingly, we observe a large velocity gradient ($47.81 pm 3.21$ km s$^{-1}$ pc$^{-1}$) across the ionised gas in a direction perpendicular to the outflow. This kinematic signature of the ionised gas shows a reasonable correspondence with the simulations of young H II regions. Based on a qualitative comparison between our observations and these simulations, we put forward a possible explanation for the velocity gradients observed in G$316.81-0.06$. If the velocity gradient perpendicular to the outflow is caused by rotation of the ionised gas, then we infer that this rotation is a direct result of the initial net angular momentum in the natal molecular cloud. If this explanation is correct, this kinematic signature should be common in other young (bipolar) H II regions. We suggest that further quantitative analysis of the ionised gas kinematics of young H II regions, combined with additional simulations, should improve our understanding of feedback at these early stages.