The structure and the energy of vortices in rotating 3He-A are considered in the presence of a weak magnetic field. It is shown, using the logarithmic approximation for the free energy, that there will be a sequence of textural transitions when the magnetic field is increased. The transition from a nonsingular texture to a singular texture is studied in detail. It is shown that the l vector is almost uniform outside the cores of vortices. To verify these results, measurements by NMR and by ultrasound are suggested.