In that case, he is referring to his skin colour, and the fact that he is Black.
So it's an American style, sarcastic joke.He's essentially saying: "Do you think I am a white person with a tan? You realise that I am black, don't you?" Implicitly, "I know what you are talking about, because I am black and I am familiar with this topic".

It always take me an eternity to understand this type of American sarcastic humour. And I think I have heard the joke with black Americans referring to having a "tan" before...
That's definitely what is going on then. There is no other explanation.