We demonstrate a simple-to-fabricate refractometer based on the inscription of fiber Bragg gratings in a special C-shaped optical fiber. The C-shaped fiber was drawn into shape using a quarter cladding removed preform of a commercial standard single-mode fiber by simple machining. The sensor did not suffer from cross-sensitivity of the refractive index with ambient temperature fluctuations, commonly occurring with many optical fiber refractometers. A refractive index sensitivity of 1300 pm per refractive index unit (RIU) was achieved without employing any additional sensitization techniques such as tapering or etching.