There are a number of distinct signatures of superfluids, one of which is the appearance of quantized vortices. There have been some attempts to understand the putative supersolid He-4 in the vortex framework, but no conclusive evidence that supports the existence of the vortices has been reported. Here, we investigate the rotation velocity dependence of the torsional oscillation of solid He-4 at various temperatures. The velocity sweep reveals intriguing periodic staircaselike features below about 300 mK. The staircase patterns show remarkable periodicity, and we interpret these patterns as a consequence of vortex injection. However, there are some features that cannot be accounted for with simple injection of vortices into superfluid, and further investigation is required.