A quasi-one dimensional antiferromagnet with a strong reduction of the ordered spin component, BaCu2Si2O7, is studied by the magnetic resonance technique in a wide field and frequency range. Besides of conventional spin-flop transition at the magnetic field parallel to the easy axis of spin ordering, magnetic resonance spectra indicate additional spin-reorientation transitions in all three principal orientations of magnetic field. At these additional transitions the spins rotate in the plane perpendicular to the magnetic field keeping the mutual arrangement of ordered spin components. The observed magnetic resonance spectra and spin-reorientation phase transitions are quantitatively described by a model including the anisotropy of transverse susceptibility with respect to the order parameter orientation. The anisotropy of the transverse susceptibility and the strong reduction of the anisotropy energy due to the quantum spin fluctuations are proposed to be the reason of the spin reorientations which are observed.