The average molecular orientation in the adsorbed water layers formed on amorphous SiO(2) in ambient conditions was determined as a function of relative humidity using polarization attenuated total reflectance infrared spectroscopy (ATR-IR). The silicon oxide surface was prepared by chemically cleaning in aqueous solution, washing with water, and drying with argon. After drying, this produced a SiO(2) surface with hydroxyl groups, giving rise to a water contact angle < 5 degrees. Primarily two types of vibrational peaks that correspond to liquid water and solid-like water were observed in the adsorbed water layers formed on this surface at room temperature. The average orientation of the water molecules was determined from the dichroic ratio of s- to p-polarization absorbances. At low relative humidities, the highly hydrogen bonded solid-like structure exhibits a dichroic ratio as low as approximately 0.4, while the liquid water structure exhibits a dichroic ratio close to approximately 1.0. As the relative humidity increases, the dichroic ratio of both water structures approaches a dichroic ratio of 0.7 approximately 0.8, which is consistent with the random orientation of molecules of bulk water and ice.