Measuring medium-range order is a challenging and important problem in the structural study of disordered materials. We have developed a new technique, fluctuation x-ray microscopy, that offers quantitative insight into medium-range correlations in disordered materials at nanometre and larger length scales. In this technique, which requires a spatially coherent x-ray beam, a series of speckle patterns are measured at a large number of locations in a sample using various illumination sizes. Examination of the speckle variance as a function of the illumination spot size allows the structural correlation length to be measured. To demonstrate this technique we have studied polystyrene latex spheres, which serve as a model for a dense random-packed glass, and for the first time have measured the correlation length in a disordered system by fluctuation X-ray microscopy. We discuss data analysis and procedures to correct for shot noise and detector noise. This approach could be used to explore medium-range order and subtle spatial structural changes in a wide range of disordered materials, from soft matter to nanowire arrays, semiconductor quantum dot arrays and magnetic materials.