The first-order (FO) perturbation theory has been widely investigated to design the digital nonlinearity compensation (NLC) technique to deal with the intra-channel fiber nonlinearity effect in coherent optical communication systems. The main advantages of the perturbation theory-based approach are the possibility of the implementation on a single stage for the entire fiber link and one sample per symbol operation. In this paper, we propose to extend the FO perturbation theory-based NLC (FO-PB-NLC) technique to the second-order (SO), referred to as the SO-PB-NLC, to enhance the NLC performance. We present a comprehensive theoretical analysis for the derivation of the SO nonlinear distortion field, which is the foundation for the SO-PB-NLC technique. Through numerical simulations, we show that the proposed SO-PB-NLC technique significantly enhances the NLC performance and the maximum transmission reach when compared to the FO-PB-NLC technique. Then, the performance of the SO-PB-NLC technique is compared with that of the benchmark digital back-propagation (DBP).