Generally, it's possible to do computing on GPUs -- some keywords to look for more might be CUDA, OpenCL, OpenACC.
The question is if it's worth it. In order to outperform the CPU, you need to exploit a GPUs massive-parallelized and vector-optimized architecture (which depends on the update pattern of your particles). Also keep in mind that both video memory and bandwidth to upload/download data to the graphics card can be limiting factors depending on your application.
Since GPU programming comes with quite some complexity, I would first try to maximize the performance on the GPU. Did you use a profiler to find the bottleneck? If the computation is stuck on one core, could you try multi-threading? Are you sure you use optimal data structures, algorithms, avoid cache misses and bad branch predictions, etc?
