The near-edge X-ray absorption fine structure (NEXAFS) of evaporated thin films of DNA nucleobases on an Au-coated Si surface at room temperature has been investigated in the regions around the nitrogen and oxygen K-edges using highly monochromatic synchrotron soft X-rays. Each nucleobase shows a specific absorption spectrum originating from the resonant excitation of 1s electrons of nitrogen or oxygen to antibonding states, some of which strongly depend on the polarization angle of incident soft X-rays. From an analysis of the polarization angle dependences of the pi* resonance absorption intensity, it is found that purines are orientated to the multilayer surface with an angle of 15 +/- 6degrees for adenine and 38 +/- 1degrees for guanine. Uracil has an orientation of 16 +/- 4degrees, although other pyrimidines such as thymine and cytosine are randomly orientated with respect to the surface. These characteristics of the obtained NEXAFS spectra not only reveal the electrical structure of the nucleobases but also provide us with knowledge of the thermal stability of the self-organized base-stacking structure, which might play an important role in retaining the conformation of an intact or base-damaged DNA molecule.