Nope, you can't use CUDA for that. CUDA is limited to NVIDIA hardware. OpenCL would be the best alternative.
Khronos itself has a list of resources. As does the StreamComputing.eu website. For your AMD specific resources, you might want to have a look at AMD's APP SDK page.
Note that at this time there are several initiatives to translate/cross-compile CUDA to different languages and APIs. One such an example is HIP. Note however that this still does not mean that CUDA runs on AMD GPUs.