I work at a large teaching facility and they *prefer* new grads. Don't worry if you didn't have the chance to do any sort of OR rotations in school. The best thing you can do would be to try to get a toe-hold in an OR where you think you'd like to work so that when you apply for a job there, you're not one of a billion faceless applicants. If you happen to know someone who works at that facility and can get you the name of an OR manager there, that's best. Call or e-mail, say you're graduating on such-and-such date and you'd like to know if you could shadow for a day in the OR, "just to see what it's like." It's non-threatening ("Hey, I'm not asking for an interview, I just want some info!") and many facilities routinely do this. Then once you are there, treat it like an interview. Be prepared with questions, be careful and courteous in the room, remember people's names, be friendly. At the end of the day, ask if you can see the manager just for a minute to thank him/her personally. Anything to get yourself remembered in a positive way. If you don't know anyone there, call HR, tell them you're thinking it's possible you might like to work in the OR one day, and could you shadow there? (Don't sound desperate, make it casual.) Just get a foot in, and then like I said, treat it like an interview. Shake hands!
New grads these days really underestimate the value of networking in finding new jobs. If you aren't able to make a shadow day happen, even just calling HR before filling out an application helps. New apps are always screened through HR first, so if the manager doesn't know you, then HR has to like you in order for the hiring manager to even get your app. Call the general HR phone number, ask for whoever does the hiring for the OR, and be very general with your questions. You don't want to come off like a missile, you just want the opportunity to build a rapport with someone who can get you hired. Be professional, have good questions, make it sound like you're just gathering information but make sure you're leaving a positive and professional impression. It's okay to say that you do want to work in the OR. The key is that whatever you do (phone call, e-mail, shadow, whatever), do it *before* you even fill out an application. At the end of your conversation, you can say, "I loved it here! Do you have any openings?" and when they say yes, you can say, "I'm definitely going to apply. Keep your eyes open!" And they'll remember you when they get the application.
Before I started in the OR, I thought there must be some magical pathway to get there; there's not, just like anywhere in nursing. It's all in who you know. Even if you don't know anyone, you can change that and make it happen.