Demand response programs help stabilize the electricity grid by providing monetary stimulus to consumers if they regulate their power consumption following market requirements. Regulation service, a market that requires participants to regulate power by following a signal updated every few seconds, is particularly beneficial to HPC data centers since data centers are capable of increasing/decreasing power consumption owing to the flexibility in running workloads and the availability of power control mechanisms. While prior works have explored how data centers can provide regulation service reserves, Quality-of-Service (QoS) provisioning for the jobs running at the data centers has not been considered. In this work, we propose an Adaptive policy with QoS Assurance that enables data centers to participate in regulation service programs with assurance on job QoS. Our policy regulates data center power through job scheduling and server power capping. QoS assurance is achieved by applying a queueing-theoretic result to our job scheduling strategy. We evaluate our policy by experiments on a real cluster. Our results demonstrate that the proposed policy reduces electricity costs by 25-56 percent while providing QoS assurance. On the other hand, the baseline policies cannot meet QoS constraints in 9 of the 14 workload traces tested.