Event-triggered and self-triggered control, in which the time of update to the controls is based on either current or outdated sampled data, have recently been employed to reduce the computational load or resource consumption for distributed real-time control systems. In this work, we propose a self-triggered scheme for nonlinear controlled stochastic differential equations with additive noise terms. A self-triggering update condition is derived that guarantees stability in the p-th moment of the state distribution. We show that the length of the times between controller updates as computed from the proposed scheme is strictly positive and provide examples.