We present a thread-modular abstract interpretation(TMAI) technique to verify programs under the release-acquire (RA) memory model for safety property violations. The main contributions of our work are: we capture the execution order of program statements as an abstract domain, and propose a sound upper approximation over this domain to efficiently reason over RA concurrency. The proposed domain is general in its application and captures the ordering relations as a first-class feature in the abstract interpretation theory. In particular, the domain represents a set of sequences of modifications of a global variable in concurrent programs as a partially ordered set. Under this approximation, older sequenced-before stores of a global variable are forgotten and only the latest stores per variable are preserved. We establish the soundness of our proposed abstractions and implement them in a prototype abstract interpreter called PRIORI. The evaluations of PRIORI on existing and challenging RA benchmarks demonstrate that the proposed technique is not only competitive in refutation, but also in verification. PRIORI shows significantly fast analysis runtimes with higher precision compared to recent state-of-the-art tools for RA concurrency.