The p$K_a$ values are important quantities characterizing the ability of protein active sites to give up protons. p$K_a$ can be measured using NMR by tracing chemical-shifts of some special atoms, which is however expensive and time-consuming. Alternatively, p$K_a$ can be calculated numerically by electrostatic free energy changes subject to the protonation and deprotonation of titration sites. To this end, the Poisson-Boltzmann (PB) model is an effective approach for the electrostatics. However, numerically solving PB equation is challenging due to the jump conditions across the dielectric interfaces, irregular geometry of the molecular surface, and charge singularities. Our recently developed matched interface and boundary (MIB) method treats these challenges rigorously, resulting in a solid second order MIBPB solver. Since the MIBPB solver uses Green's function based regularization of charge singularities by decomposing the solution into a singular component and a regularized component, it is particularly efficient in treating the accuracy-sensitive, numerous, and complicated charge distributions from the p$K_a$ calculation. Our numerical results demonstrate that accurate free energies and p$K_a$ values are achieved at coarse grid rapidly. In addition, the resulting software, which pipelines the entire p$K_a$ calculation procedure, is available to all potential users from the greater bioscience community.