We propose and numerically demonstrate chaos synchronization of two vertical-cavity surface-emitting lasers (VCSELs) induced by common injection of constant-amplitude random-polarization light for physical key distribution. Results show that synchronization is sensitive to polarization rotation of injection light, and synchronization coefficients larger than 0.9 can be achieved as the rotation-degree mismatch is smaller than ±10°. Therefore, polarization rotation degree can serve as a hardware key parameter. Furthermore, each laser’s output has no correlation to the constant amplitude of the injected light. Their components with identical polarization state, e.g. x or y polarization of VCSEL, also have low correlation coefficient smaller than 0.2. It is therefore believed that this synchronization scheme can provide a security-enhanced method of physical key distribution.