We theoretically explore the impact of cross-Kerr nonlinearity (CKN) on rotary photon drag (RPD) and temporal cloaking in a Sagnac interferometer. With the activation of CKN, significant improvements in RPD and temporal cloaking are observed. Drag angles of ±1×10−3 and±5×10−3 radians are attained. Similarly, temporal gaps of 10µs, 12µs and 13µs are noticed. In addition to the observed electromagnetically induced transparency (EIT) window, group refractive index is drastically enhanced, time delay/advance are tuned from pico-radians to micro-radians, and reduced relativistic group velocities are achieved by activating CKN in the system. Additionally, the transmission pulses intensities are noticed to reduce with the dragging phenomenon. The findings may have potential applications in controlled image coding, rotation sensing and secure communication technologies.