In this paper, the \(J\)-spectral factorization problem for para-Hermitian rational matrix functions is studied. A rational matrix function \(G\) is called para-Hermitian if \(G(\lambda)=G(\overline{- \lambda})^*\) for every \(\lambda\in \mathbb C\) except for the poles of \(G\). Given a realization of \(G\) of the form \(G(\lambda)=J + C(\lambda I-A)^{-1}B\), where \(J\) is a signature matrix satisfying \(J=J^*=J^{-1}\), necessary and sufficient conditions for the existence of a \(J\)-spectral factorization are given. The \(J\)-spectral factorization problem is the question whether there there exists a rational matrix function \(W\) satisfying \(G(\lambda)= W(-\overline{\lambda})^*J W(\lambda)\). Necessary and sufficient conditions are given in terms of the matrices \(A, B, C\) and \(J\). An algorithm for obtaining the \(J\)-spectral factor \(W\) is developed and examples are included as well.