Gold nanoparticles deposited on indium-tin-oxide coated substrates show substantial circularly polarized acoustically induced light gyration (AILG) at liquid-helium temperature. The effect was observed only during simultaneous treatment by two coherent acoustic waves with basic frequencies of 0.8-1.6 MHz and corresponding coherent double-frequency acoustical components. It was found that increasing the basic acoustical frequency to 1.6 MHz led to suppression of the effect. ATi:sapphire laser with a pulse duration of approximately 80 fs allowed us to achieve the maximal value for the AILG. Enhancement of the pulse duration higher than 200 fs also substantially diminished the effect. The maximally achieved value of the AILG susceptibility (described by a fourth-order axial tensor) caused by the circularly polarized acoustical probe field at an acoustical power density of approximately 3 W/cm2 at T = 4.2 K was equal to approximately 7.8 deg/mm for the circular acoustical wave polarization. The maximal AILG coefficient is achieved for samples that possess minimal resistivity. The investigated composites possess an acoustically induced helicoidal grating that disappeared 20 s after switching off the acoustical fields.