My friend worked in MS night shift and once a week in the morning after her shift ended, she would show up in OR (in her hospital) to say hi to everyone. She talked to the manager about how she wants to be in OR and how she understands that they are not hiring but she just wants to talk about her dream. She popped up in OR to say hi for months. Everyone knows her.
I agree with ScrubRNwannabe. The OR needs to see your face and know you're interested. I was working on a surgical floor as a new grad but knew I wanted to be in the OR. I went to the OR for a day to observe per the new grad orientation on the floor and took the opportunity to let them know I wanted to be a part of their team. I spoke with the nurses, manager, and director. I busted my butt the entire day helping as much as I could from foleys to turnovers to scrapping blood off the mayo stands. I asked tons of questions and followed up my observation day with emails. Lo and behold I got an interview a month later and have been in the OR ever since!
Also, does the OR at your facility offer an AORN Periop 101 program? If not, look for the course in your area. The Mayo Clinic/Mayo School of Health Sciences offers a fellowship in perioperative nursing that includes the AORN cirriculum, perhaps there is something similar at a facility near you.
If and when your hospital has a job fair the nurse managers and directors are usually present there. That would definitely be an opportunity to say hi when they are not busy since they usually have 7-4pm schedules.