[en] On the basis of an earlier analysis of the disorientation of a nucleus following the emission of neutrons and γ quanta in nuclear reactions, a simple model is proposed for the calculation of the spin orientation of spontaneously fissioning isomers produced in reactions with α particles. The model is used to determine the spins of spontaneously fissioning isomers from the experimental data on the anisotropy of the angular distribution of the fission fragments. In the case when there are two isomeric states in the second well, their spins are also determined from the experimental data on the ratio of the cross section (the isomer ratio for the second well)