We have demonstrated experimentally the application of an imaging plate for registering the angular distribution of parametric X-ray radiation. The imaging plate was used as a two-dimensional position-sensitive X-ray detector. High-quality images of the fine structure in the angular distributions of the yield around the reflection of the parametric X-ray radiation produced in a silicon crystal by a 255-MeV electron beam from a linear accelerator have been observed in the Laue geometry. A fairly good agreement between results of measurements and calculations by the kinematic theory of parametric X-ray radiation is shown. Applications of the imaging plates for the observation of the angular distribution of X-rays produced by accelerated particles in a crystal are also discussed.