Percy has always been attracted to athletic women. His family would probably be rather shocked to learn this, given that Percy isn't remotely athletic, but it's true. Even Penelope, studious though she was and is, had enjoyed casual games of Quidditch whenever she got a chance.
So when he happened to meet Katie Bell outside Quality Quidditch Supplies one day, he seized the chance to catch up with her, as an old acquaintance. As they talked, his attraction to her grew, until finally he mustered the courage to ask her out.
Nobody was more surprised than Percy when she accepted.