Is it possible to rotate the flange?

The old one is kind of rusty and I don't think it will budge more than 1/4 inch as someone said on another question....but would it be possible to put a new flange in? We'd like to rotate the toilet 90 degrees if possible.

There are possibilities, some of which would depend on what materials the pipe and flange are, and what the layers of the floor consist of.

Code requires 15" clearance from the centerline to either side of a toilet. Given (most common) the flange is 12" from the wall, turning it without moving it would not be code compliant since it would only be 12" to the wall. Anything's possible, it just depends on what's there, and how much you want to spend.