This paper is devoted to Fraunhofer diffraction by hexagonal ice crystals like those that can be encountered in cirrus clouds. Such crystals are important, for they are the basic building elements of crystals of more complex shape. A new alternative based on the Maggi-Rubinowicz transformation is proposed. This technique, whose basic formula is a line integral version of the Kirchhoff integral, is very easy to implement and is not time consuming. Diffraction patterns of hexagonal ice crystals with (i) fixed arbitrary orientation, (ii) random orientation, and (iii) preferred orientation are given. The topic is of importance since the radiative impact of cirrus clouds, which depends directly on ice crystal optical properties, is still a challenging problem in climate research.