We present the design and calibration of a spectroscopic sensitive polarimeter. The polarimeter can measure the full Stokes vector in the wavelength range 550 to 750 nm with 1-nm resolution and consists of a fiber-based spectrophotometer, a white light emitting diode light source, two liquid crystal retarders, and one polarizer. Calibration of the system is achieved with a scheme that does not require knowledge of the polarizing elements’ orientation or retardation. Six intensity spectra are required to calculate the full spectrum Stokes vector. Error in the polarimeter is less than 5%. We report the Stokes vectors for light transmitted through nonscattering polarizing elements as well as a measurement of the depolarizing properties of chicken muscle at several wavelengths.