Aims. High-energy irradiation of circumstellar material might impact the structure and the composition of a protoplanetary disk and hence the process of planet formation. In this paper, we present a study of the possible influence of stellar irradiation, indicated by X-ray emission, on the crystalline structure of circumstellar dust. Methods. The dust crystallinity is measured for 42 class II T Tauri stars in the Taurus star-forming region using a decomposition fit of the 10 mu m silicate feature, measured with the spitzer IRS instrument. Since the sample includes objects with disks of various evolutionary stages, we further confine the target selection, using the age of the objects as a selection parameter. Results. We correlate the X-ray luminosity and the X-ray hardness of the central object with the crystalline mass fraction of the circumstellar dust and find a significant anti-correlation for 20 objects within an age range of approx. 1 to 4.5 Myr. We postulate that X-rays represent the stellar activity and consequently the energetic ions of the stellar winds which interact with the circumstellar disk. We show that the fluxes around 1 AU and ion energies of the present solar wind are sufficient to amorphize the upper layer of dust grains very efficiently, leading to an observable reduction of the crystalline mass fraction of the circumstellar, sub-micron sized dust. This effect could also erase other relations between crystallinity and disk/star parameters such as age or spectral type.