From a legal/process standpoint, there's no problem with resigning your spot and reapplying for a new position in the same field.
From a practical standpoint, it's a very risky option. You could try to get a new PGY1 (or PGY2 for advanced specialties, like radiology) position via the match. This creates a potential funding problem for you, and as mentioned above it's not clear that your application would be any better the second time around. You could try to switch programs at the same PGY level -- i.e. complete a PGY-2 at one program, and then move into a PGY-3 at another. This is always a possibility, involves having a supportive PD since your switch then leaves your first program with an opening.
Bottom line is you could end up losing your current position and not getting a new one. You need to decide whether your current situation is bad enough that it is worth the risk.