Yes, it’s definitely worth a shot. You have the grades, scores and curriculum, you just have to put it together.
You might want to get in touch with Jocelyn Goldfein. She’s a 1997 Stanford grad and former CS major who has had a successful technology career, including executive positions at VMWare and Facebook, and who has a strong interest in mentoring women in computer science. She can be found on LinkedIn and Facebook, and might have some thoughts on how to position yourself specifically for Stanford.