We present a theory for the spin correlation function of the t - J model in the framework of the dynamical mean-field theory. Using this mapping between the lattice and a local model we are able to obtain an intuitive expression for the nonlocal spin susceptibility, with the corresponding local correlation function as input. The latter is calculated by means of local Goldstone diagrams following closely the procedures developed and successfully applied for the (single-impurity) Anderson model. We present a systematic study of the magnetic susceptibility and compare our results with those of a Hubbard model at large U. Similarities and differences are pointed out and the magnetic phase diagram of the t - J model is discussed.