An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer (PST for short) and multiple state transfer (MST for short) on integral oriented circulant graphs. Specifically, a characterization of PST (or MST) on integral oriented circulant graphs is provided. As an application, we also obtain a closed-form expression for the number of integral oriented circulant graphs with fixed order having PST (or MST).