The formation of gallium nitride (GaN) semi-polar and non-polar nanostructures is of importance for improving light extraction/absorption of optoelectronic devices, creating optical resonant cavities or reducing the defect density. However, very limited studies of nanotexturing via dry etching have been performed, in comparison to wet etching. In the paper associated with this dataset, we investigate the formation and morphology of semi-polar (11-22) and non-polar (11-20) GaN nanorods using inductively coupled plasma (ICP) etching. The impact of gas chemistry, pressure, temperature, radio-frequency (RF) and ICP power and time are explored. The scanning electron microscopy images contained in this dataset indicate that a chemical component of the etch process is found to have a significant impact on the morphology, being impacted by the polarity of the planes. In contrast, the images show that increasing the physical component enables the impact of crystal orientation to be minimized to achieve a circular nanorod profile with inclined sidewalls. These conditions were obtained for a small percentage of chlorine (Cl2) within the Cl2 + argon (Ar) plasma combined with a low pressure. Damage to the crystal was reduced by lowering the direct current (DC) bias through a reduction of the RF power and an increase of the ICP power.