The critical need to study the magnetic field in the solar corona is highlighted by recent observational facilities, such as the Daniel K. Inouye Solar Telescope and Aditya-L1. A powerful tool for probing the magnetism of the solar corona is forward modeling of the intensity and polarization of coronal emission lines in three-dimensional (3D) magnetohydrodynamic models. Here we present P-CORONA, a new spectral synthesis code designed to calculate the intensity and polarization of coronal lines in 3D models of the solar corona, taking into account the symmetry breaking induced by magnetic and velocity fields. P-CORONA allows the calculation of the on-disk and off-limb intensity and polarization of forbidden and permitted coronal lines, thus facilitating a wide range of investigations. Applying the quantum theory of atom–photon interactions, P-CORONA accounts for the spectral line polarization caused by anisotropic radiation pumping and the Hanle and Zeeman effects, making it a valuable tool for investigating coronal magnetic fields. This paper details the code's theoretical formulation, implementation, and illustrative results of calculations in different 3D coronal models (MURaM and Predictive Science Inc.), including the impact of the Zeeman effect from the transverse magnetic field component on selected coronal forbidden lines. P-CORONA is now accessible to the research community on GitLab and Zenodo, providing a resource to facilitate research aimed at advancing our understanding of coronal magnetism and dynamics.