Spin-orbit coupling (SOC) effects in non-centrosymmetric systems lead to a uniform spin configuration in momentum space known as persistent spin texture (PST). The PST has been predicted to support an extraordinarily long spin lifetime of carriers promising for spintronics applications. Using density functional theory, we report the existence of PST in nitrogen-based perovskite (CeTaN₃), a non-centrosymmetric ferroelectric material with spontaneous polarization of 5.6 μC/cm² along [100] direction. Our calculations showed that CeTaN₃ is a direct band gap (0.436 eV) semiconductor and exhibits PST both in the conduction and valence bands. The calculated Rashba parameter was 0.399 eVÅ (0.282 eVÅ) for the conduction (valence) band. A comprehensive investigation of the stability of CeTaN₃ was performed by calculating its elastic constants, reaction decomposition enthalpy, and phonon dispersion. All three methods showed that CeTaN₃ is stable. We also investigated the effects of the hydrostatic pressure on the spin splitting of the bands. We found that CeTaN₃ preserved the PST up to 6 GPa and the splitting of the bands disappeared at 8 GPa. The present study paves the way for using external pressure as a prime factor in tuning not-yet-synthesized perovskite materials suitable for spintronics and optoelectronic applications.