The Ray-Tracing (RT) core has been widely integrated into modern GPUs to accelerate ray-tracing rendering. Recent research shows that RT cores can also be repurposed to accelerate non-rendering workloads. Since the RT core is essentially a hardware Bounding Volume Hierarchy (BVH) tree traversal accelerator, it has the potential to significantly boost the performance of spatial workloads. However, the specialized RT programming model makes it challenging to utilize RT cores for these tasks. Having inspired by the core functionality of RT cores, we design and implement RTSpatial, a spatial index library that accelerates spatial queries on RT cores. RTSpatial supports both point and range queries, and is also mutable to adapt to changing data. Rather than relying on a case-by-case approach, RTSpatial is a framework designed to offer a generic and fast spatial index for spatial data processing. By formulating the queries as RT-suitable problems and overcoming load balancing challenges, RTSpatial delivers superior query performance through RT cores without requiring developers to do sophisticated programming on this specialized hardware. RTSpatial outperforms CPU and GPU spatial libraries by up to 11.7x for point queries, 93.2x for range-contains queries, and 13.7x for range-intersects queries. RTSpatial also surpasses the state-of-the-art RT method by up to 3.8x for the point-in-polygon test.