Depending on your community, your age, your perspective on things, this may or may not even be an issue. I grew up in a diverse town where different skin tones mingled an dated all the time. I've also lived in places where that's not the norm. Luckily, I'm back in Brooklyn, and again, it's not uncommon.
Bottom line is, you are a woman and he's a man. If you guys interact there will be (or not be) attraction and vibe between the two of you. Race, though a component, doesn't have to be the overarching identity mark here. Does it? Again, this goes back to... is your environment very segregated? Are you the only person of color in your social scene? And who is this white fella? How well do you know him and his dating likes and dislikes. Often we create narratives for people before we even know what the deal is as a means to protect ourselves.
"How do I make him as me out?" You don't. You be you around him. You initiate conversation, feel good about yourself and see where things go. If the vibe is there - you can ask him out.
Let us know how it goes. And as Cyndi Lauper reminded us a few years back, show him your true colors.
Or ask HIM out...
I'd say that is hardly ever a deal breaker. I thought I was never attracted to black guys, until I met my ex-boyfriend. It wasn't that I had anything against them I just thought I was not attracted to them. Yet he totally shattered that thought. I've heard similar stories from other people - we keep wanting to fit people into types but its silly to try and do that. Its more a question of is he attracted to you rather than who's he's dated in the past or even thinks he wants to date. I'd say spend time with him and see what happens but there are a lot of more important factors than race going on if a guy will like you or not.