Electrical properties of silicon doped AlN nanowires grown by plasma assisted molecular beam epitaxy were investigated by means of temperature dependent current–voltage measurements. Following an Ohmic regime for bias lower than 0.1 V, a transition to a space-charge limited regime occurred for higher bias. This transition appears to change with the doping level and is studied within the framework of the simplified theory of space-charge limited current assisted by traps. For the least doped samples, a single, doping independent trapping behavior is observed. For the most doped samples, an electron trap with an energy level around 150 meV below the conduction band is identified. The density of these traps increases with a Si doping level, consistent with a self-compensation mechanism reported in the literature. The results are in accordance with the presence of Si atoms that have three different configurations: one shallow state and two DX centers.