Isomeric yield ratios of Sb-128(5(+), 8(-)), Sb-130(4(+), 8(-)), I-132(4(+), 8(-)), I-134(4(+), 8(-)), and I-136(2(-), 6(-)) isomer pairs in the spontaneous fission of Cf-252 were measured and the angular momenta J(rms) of primary fission fragments were deduced from the isomeric yield ratios obtained. The deduced J(rms) for each nuclide in the spontaneous fission of Cf-252 is about the same as that found in the thermal neutron induced fission. A discussion is made by comparing the angular momenta deduced with those from other various fissioning systems.