We have designed and implemented a fiber optic shape sensor for high-energy ionizing environments based on multicore optical fibers. We inscribed two fiber Bragg gratings arrays in a seven-core optical fiber. One of the arrays has been inscribed in a hydrogen-loaded fiber and the other one in an unloaded fiber in order to have two samples with very different radiation sensitivity. The two samples were coiled in a metallic circular structure and were exposed to gamma radiation. We have analyzed the permanent radiation effects. The radiation-induced Bragg wavelength shift (RI-BWS) in the hydrogen-loaded fiber is near ten times higher than the one observed for the unloaded fiber, with a maximum wavelength shift of 415 pm. However, the use of the multiple cores permits to make these sensors immune to RI-BWS obtaining a similar curvature error in both samples of approximately 1 cm without modifying the composition of the fiber, pre-irradiation or thermal treatment.