The automation of forest field reference data collection has been an intensive research objective for laser scanning scientists ever since the invention of terrestrial laser scanning more than two decades ago. In this study, we demonstrated that an under-canopy UAV laser scanning system utilizing a rotating laser scanner can alone provide accurate estimates of canopy height and stem volume for the majority of trees in a boreal forest. We mounted a rotating laser scanner based on a Velodyne VLP-16 sensor onboard a manually piloted UAV. The UAV was commanded with the help of a live video feed from the onboard camera. Since the system was based on a rotating laser scanner providing varying view angles, all important elements such as treetops, branches, trunks, and ground could be recorded with laser hits. In an experiment including two different forest structures, namely sparse and obstructed canopy, we showed that our system can measure the heights of individual trees with a bias of −20 cm and a standard error of 40 cm in the sparse forest and with a bias of −65 cm and a standard error of 1 m in the obstructed forest. The accuracy of the obtained tree height estimates was equivalent to airborne above-canopy UAV surveys conducted in similar forest conditions or even at the same sites. The higher underestimation and higher inaccuracy in the obstructed site can be attributed to three trees with a height exceeding 25 m and the reduced point density of these tree tops due to occlusion and the limited ranging capacity of the scanner. Additionally, we used our system to estimate the stem volumes of individual trees with a standard error at the level of 10%. This level of error is equivalent to the error obtained when merging above-canopy UAV laser scanner data with terrestrial point cloud data. The results show that we do not necessarily need a combination of terrestrial point clouds and point clouds collected using above-canopy UAV systems in order to accurately estimate the heights and the volumes of individual trees in reference data collection.