It's not just cats, but it seems like it's more animals in general. I think, because of our socialization troubles, gives us a sense of loneliness, and animal companions such as dogs and cats tend to keep us company. If you think about it, they're easy to talk to, they don't think any weird of you, for some of the things you say, do, or think, and they love you unconditionally.
And I think cats are associated with aspergers, because they're calm, and quiet. They don't bark, and their meows are too quiet to stress out an aspie with noise.
I'm no aspie, but I do have a mild case of autism that people often mistake for aspergers. While I am a dog lover, I also love cats, because they're quiet, calm, and can be just as affectionate as dogs, just in a different way. (Don't have any because my mom is allergic) I've observed some of my aspie friends, and most of them prefer quietness over noise. My moderately autistic nephew is also afraid of dogs, but he loves cats. (Animals in general, too... Except for dogs)
So this has brought me to the conclusion, that because of it's calm and quiet behavior, it makes the cat a loved companion to many aspie or autistic people. (At least for the ones who don't like dogs)