In this paper, discrete-time adaptive control of linearly parameterized fully actuated Port-controlled Hamiltonian systems with parameter uncertainties in energy function is considered. A discrete-time adaptive interconnection and damping assignment passivity-based control (IDA-PBC) method, utilizing the immersion and invariance (I&I) approach, for the considered uncertain Hamiltonian system, is presented. A discrete-time parameter estimator based on the immersion and invariance approach is derived to obtain an automatic tuning mechanism for the IDA-PBC controller. The stability analysis for the estimator and the closed-loop system is done using the Lyapunov theory. The proposed method is applied to two fully actuated physical systems and its performance is tested by simulations. Simulation results show that the proposed I&I-based adaptive IDA-PBC controller successfully preserves the performance of the IDA-PBC controller designed with true parameters under a large amount of uncertainty.