We report a new technique for torsional testing of materials under giga-pascal pressures, which uses a shearing module in a large volume Paris-Edinburgh press in combination with highresolution fast radiographic X-ray imaging. The measurement of the relative amplitude and phase lag between the cyclic displacement in the sample and a standard material (Al2O3) provides the effective shear modulus and attenuation factor for the sample. The system can operate in the 0.001 to 0.01 Hz frequency range, and up to 5 GPa and 2000 K; although hightemperature measurements may be affected by grain growth and plastic strain. Preliminary experimental results on San Carlos olivine are in quantitative agreement with previously reported Q-1 factors at lower pressure. This cyclic torsional loading method opens new directions to quantify the viscoelastic properties of minerals/rocks at seismic frequencies and in pressure-temperature conditions relevant to the Earth's mantle, for a better interpretation of seismological data.