Summary: Let \(R\) be a commutative principal ideal domain (PID) with \(\text{char} (R) \neq 2\), \(n \geq 2\). Denote by \(\mathcal S_n(R)\) the set of all \(n\times n\) symmetric matrices over \(R\). If \(\phi\) is a Jordan automorphism on \(\mathcal S_n(R)\), then \(\phi\) is an additive rank preserving bijective map. In this paper, every additive rank preserving bijection on \(\mathcal S_n(R)\) is characterized, thus \(\phi\) is a Jordan automorphism on \(\mathcal S_n(R)\) if and only if \(\phi\) is of the form \(\phi(X) = \alpha^tPX^\sigma P\) where \(\alpha\in R^*\), \(P\in \text{GL}_n(\mathbb R)\) which satisfies \({}^tPP = \alpha^{-1}I\), and \(\sigma\) is an automorphism of \(R\). It follows that every Jordan automorphism on \(\mathcal S_n(R)\) may be extended to a ring automorphism on \(M_n(\mathbb R)\), and \(\phi\) is a Jordan automorphism on \(\mathcal S_n(R)\) if and only if \(\phi\) is an additive rank preserving bijection on \(\mathcal S_n(R)\) which satisfies \(\phi(I) = I\).