At first glance, I would say the rail is even lower than on an AR (relative to the stock). AR rings are typically 1" tall, I would guess you need about 1.125-1.25" tall rings. Does Barrett make them that high?
Another point of reference: I shoot a Ferret50 (AR15 barreled upper) and use 0.6" rings to hold a 34 mm scope tube. The rail is taller (0.8" above the receiver) than your rifle and the check piece is adjustable. I have the rail set at the lowest height.