In this work, we present a novel self-supervised method for Low Dose Computed Tomography (LDCT) reconstruction. Reducing the radiation dose to patients during a CT scan is a crucial challenge since the quality of the reconstruction highly degrades because of low photons or limited measurements. Supervised deep learning methods have shown the ability to remove noise in images but require accurate ground truth which can be obtained only by performing additional high-radiation CT scans. Therefore, we propose a novel self-supervised framework for LDCT, in which ground truth is not required for training the convolutional neural network (CNN). Based on the Noise2Inverse (N2I) method, we enforce in the training loss the equivariant property of rotation transformation, which is induced by the CT imaging system, to improve the quality of the CT image in a lower dose. Numerical and experimental results show that the reconstruction accuracy of N2I with sparse views is degrading while the proposed rotational augmented Noise2Inverse (RAN2I) method keeps better image quality over a different range of sampling angles. Finally, the quantitative results demonstrate that RAN2I achieves higher image quality compared to N2I, and experimental results of RAN2I on real projection data show comparable performance to supervised learning.