I like Fendle's idea, where you could basically just do something that is already romantic like a dinner date and ask her there. It's usually quite an effective scenario because of a romantic mood and setting
Another cool idea would be to set up a surprise for her where you could ask her. For example, if you have a favourite outdoor spot you two like to go, or a spot where you met that means a lot to you, you could set something up there with flowers, a large banner that says "will you go to prom with me" etc, a picnic with some lit candles (if you do it at night) and a blanket, and you could lure her there so that when she walks in, the romantic setting & the banner ask the question for you.
If you are really scrapped for ideas, I know it sounds cheesy and lame but you could also try looking on Youtube. I was on some kid's channel ages ago and he had a video where he asked his GF to prom, and I watched it. It ended up bringing a ton of related videos up along the side, and I was surprised how many people film their daring/romantic efforts at getting a date for prom and put it on the internet. Who knows, it may give you some ideas!