We propose and demonstrate novel band-rejection filtering scheme based on lossy torsional acousto-optic (AO) coupling in a single polarization fiber. Simulation results show that the polarization insensitive notch depth of -30dB is achievable for a 2-m-long fiber in the state-of-theart fiber manufacturing technology. More efficient band-rejection in excess of -44dB could be also feasible in practical fiber length. Good agreement between our numerical simulations and proof-of-principle experiments is obtained in optical communication C-band. The measured notch depth is -29.4dB for a low loss polarization mode after propagating an AO interaction length of 49.8 cm. The filtered wavelength could be tuned linearly by the variable acoustic transducer frequency with the slope of 0.61 nm/kHz, and the polarization dependence of notch depth was measured to 0.8dB in our setup. Our experiments confirm the validity and practicality of the approach, and illustrate the in-fiber torsional AO band-rejection filter with simpler device configuration is achievable.