In this paper, we presented a discrete-time adaptive Passivity Based Control (PBC) for linearly parametrized port-controlled Hamiltonian systems with additive uncertainty. For the parameter estimation we exploited the Immersion and Invariance approach to achieve an automatic tuning for the designed PBC controller. The locally asymptotic stability of the closed loop system under PBC control with proposed parameter estimator is shown using Lyapunov theory. Simulations are carried out to test performance of proposed adaptive control method. Results illustrates that the estimator successfully estimates the uncertain parameters and the PBC utilizing this parameters stabilizes the closed loop system and preserve the performance of certainty equivalent controller.