Polarization-entangled photon pair sources exhibiting nonlocal quantum correlations are crucial to developments of quantum computing, quantum communications, quantum cryptography, and quantum sensing technologies. On-chip polarization entanglement generation thus constitutes one enabling component for integrated quantum photonic circuits. Here, we present to our knowledge the first polarization-entangled photon pair sources in a silicon nitride platform for integrated quantum photonic circuits. We demonstrate the generation of a polarization-entangled state by adopting a configuration comprising dual microring resonators, with nearly degenerate transverse electric and transverse magnetic polarized cavity resonances for the two resonators coupled in series to a common bus waveguide. We measure two-photon interference and quantum state tomography to characterize the polarization entanglement of the generated state and to reconstruct the density matrix. Our experiments reveal a visibility of 96.4% ± 3.1% and of 86.7% ± 3.2% with the |H⟩ and |V⟩ bases, respectively (and a visibility of 89.4% ± 6.6% and 81.3% ± 7.3% with the |D⟩ and |A⟩ bases), and a fidelity of ∼75.7% from the tomographic reconstructed density matrix.