The magnetic anisotropy of La0.7Sr0.3MnO3 nanopowders was measured as a function of temperature by the modified singular point detection technique. In this method singularities indicating the anisotropy field were determined analyzing ac susceptibility data. The observed relationship between temperature dependence of anisotropy constant and temperature dependence of magnetization was used to deduce the origin of magnetic anisotropy in the nanopowders. It was shown that magnetic anisotropy of La0.7Sr0.3MnO3 nanopowder is determined by two-ion (dipolar or pseudodipolar) and single-ion mechanisms.