Reliable operation of photonic integrated circuits at cryogenic temperatures would enable new capabilities for emerging computing platforms, such as quantum technologies and low-power cryogenic computing. The silicon-on-insulator platform is a highly promising approach to developing large-scale photonic integrated circuits due to its exceptional manufacturability, CMOS compatibility and high component density. Fast, efficient and low-loss modulation at cryogenic temperatures in silicon, however, remains an outstanding challenge, particularly without the addition of exotic nonlinear optical materials. In this paper, we demonstrate DC-Kerr-effect-based modulation at a temperature of 5 K at GHz speeds, in a silicon photonic device fabricated exclusively within a CMOS process. This work opens up the path for the integration of DC Kerr modulators in large-scale photonic integrated circuits for emerging cryogenic classical and quantum computing applications.