The measurement of ionizing radiation (IR) is a crucial issue in different areas of interest, from environmental safety and industrial monitoring to aerospace and medicine. Optical fiber sensors have recently proven good candidates as radiation dosimeters. Here we investigate the effect of IR on germanosilicate optical fibers. A piece of Ge-doped fiber enclosed between two fiber Bragg gratings (FBGs) is irradiated with gamma radiation generated by a 6 MV medical linear accelerator. With respect to other FBG-based IR dosimeters, here the sensor is only the bare fiber without any special internal structure. A near infrared laser is frequency locked to the cavity modes for high resolution measurement of radiation induced effects on the fiber optical parameters. In particular, we observe a variation of the fiber thermo-optic response with the radiation dose delivered, as expected from the interaction with Ge defect centers, and demonstrate a detection limit of 360 mGy. This method can have an impact in those contexts where low radiation doses have to be measured both in small volumes or over large areas, such as radiation therapy and radiation protection, while bare optical fibers are cheap and disposable.