The fast and precise selective sensing of DNA nucleobases is a longpursued method that can lead to huge advances in the field of genomics and have an impact on aspects such as the prevention of diseases, health enhancement, and, in general, all types of medical treatments. We present here a new type of nanoscale sensor based on carbon nanotubes with a specific geometry that can discriminate the type of nucleobase and also its angle of orientation. The proper differentiation of nucleobases is essential to clearly sequence DNA chains, while angular discrimination is key to improving the sensing selectivity. We perform first-principle and quantum transport simulations to calculate the transmission, conductance, and current of the nanotube-based nanoscale sensor in the presence of the four nucleotides (A, C, G, and T), each of them rotated 0, 90, 180, or 270°. Our results show that this system is able to effectively discriminate between the four nucleotides and their angle of orientation. We explain these findings in terms of the interaction between the phosphate group of the nucleotide and the nanotube wall. The phosphate specifically distorts the electronic structure of the nanotube depending on the distance and the orientation and leads to nontrivial changes in the transmission. This work provides a method for finer and more precise sequential DNA chains.