We consider a two-phase decode-and-forward (DF) relay network assisted by an unmanned aerial vehicle (UAV), where the UAV performs energy harvesting and information decoding simultaneously with a power splitting (PS) receiver structure. For the network, we optimize the PS and time allocation (TA) factors to minimize the outage probability in transferring the data from a source to a destination suffering from blockages in the direct link. The optimal solution is found in two steps, optimization of the PS factor for given TA and then optimization of the TA factor using the conditionally optimized PS factor given in a closed-form. To reduce the complexity of the optimal method, we next propose a suboptimal method using a fixed TA determined by the transmission rate only and a fixed PS ffactor given by a function of the average power of the UAV-to-destination channel. The outage probability of the proposed method is analyzed in a generalized UAV channel model including path-loss, shadowing, and Nakagami-m fading, which is shown to agree with the simulation results and is close to the optimal performance. In addition, the optimal UAV position is investigated in various channel environments, which reveals that the optimal altitude depends on the deployment scenarios and the optimal ground position is the center-point between the source and destination in general.