Although originally developed primarily for artificial intelligence workloads, RISC-V-based accelerators are also emerging as attractive platforms for high-performance scientific computing. In this work, we present our approach to accelerating an astrophysical $N$-body code on the RISC-V-based Wormhole n300 card developed by Tenstorrent. Our results show that this platform can be highly competitive for astrophysical simulations employing this class of algorithms, delivering more than a $2 \times$ speedup and approximately $2 \times$ energy savings compared to a highly optimized CPU implementation of the same code.