Feline DNA testing does exist to screen for various genetic disease, determine parentage, positive identification and various traits. There are quite a few companies and organizations that provide this service, here are a few:
- Washington State University College of Veterinarian Medicine (also a good source for information)
- Animal DNA Laboratory
- DDC Veterinary
And in case you want to do some fascinating and heavy reading on the feline genome, you can find the full text article here: Initial sequence and comparative analysis of the cat genome.