The effect of thermal annealing atmosphere on the electrical characteristics of Zinc oxide (ZnO) nanorods/p-Silicon (Si) diodes is investigated. ZnO nanorods are grown by low-temperature aqueous solution growth method and annealed in Nitrogen and Oxygen atmosphere. As-grown and annealed nanorods are studied by scanning electron microscopy (SEM) and photoluminescence (PL) spectroscopy. Electrical characteristics of ZnO/Si heterojunction diodes are studied by current-voltage (I-V) and capacitance-voltage (C-V) measurements at room temperature. Improvements in rectifying behaviour, ideality factor, carrier concentration, and series resistance are observed after annealing. The ideality factor of 4.4 for as-grown improved to 3.8 and for Nitrogen and Oxygen annealed improved to 3.5 nanorods diodes. The series resistances decreased from 1.6 to 1.8 times after annealing. An overall improved behaviour is observed for oxygen annealed heterojunction diodes. The study suggests that by controlling the ZnO nanorods annealing temperatures and atmospheres the electronic and optoelectronic properties of ZnO devices can be improved.