The effect of atmospheric scintillations on an image centroid is investigated by means of computer simulations. The simulations were performed for the case of weak turbulence for both varying and constant Cn2 (vertical and horizontal radiation propagation). It is shown that, under weak-turbulence conditions, the magnitude of the effect does not exceed 15%. However, because it grows up with the increasing turbulence, a quite strong effect of scintillations on the image centroid under the strong-turbulence conditions can be expected. A comparison of the results for vertical and horizontal propagation shows that there is no strong dependence of the effect magnitude on the structure of the Cn2 profile. Probably, it is mainly determined by two parameters: integral turbulence (Fried parameter) and scintillation level (log-amplitude variance).