I am trying to acquire XTR M975 brakes and was wondering if they would work with the current rotors I have on.
I believe that Shimano Brakes use a slightly different sized rotor. Ex. 180mm (Shimano) vs 185mm (Avid)
160mm size should be fine between shimano/avid brands. Just make sure you match the brake mount to the caliper. beast64 is correct. The "7 inch" rotors can be 180mm (shimano), 183mm (hope), 185mm (avid), etc. I believe the 203mm size is consistent between brands, but I never run them, so I have no personal experience.
Also, Avid and Hayes rotors are a bit thicker than Shimano rotors, but it's not a problem or concern.