short answer:
no.
long answer:
in order to do what you want, you would need a box with some electronics, not just an adapter cable. I don't think those exist yet, and it's such a small market, they might not ever.
The connector on the computer already has the correct data for an HDMI / DVI / VGA connection, which is why it's easier to go the other way.
you could get the video signal into your computer, and then use it that way, but the quality would not be so good, and there would be lag which I'm guessing you probably don't want with a gaming console.