This paper presents robustness properties of LQ regulators for linear time-invariant systems with delay in the input. The Kalman inequality concerning the return difference matrix is derived, and the stability margins of LQ regulators are investigated when the open-loop systems are stable. In order to obtain the stability margins of LQ regulators, an upper bound of the solution of LQ Riccati equations is derived. Finally, the LQG/LTR method for the robustness improvement of LQG regulators is obtained and illustrated with an example.