This paper studies an online replication problem for distributed data access. The goal is to dynamically create and delete data copies in a multi-server system as time passes to minimize the total storage and network cost of serving access requests. We study the problem in the emergent learning-augmented setting, assuming simple binary predictions about inter-request times at individual servers. We develop an online algorithm and prove that it is ($\frac{5+α}{3}$)-consistent (competitiveness under perfect predictions) and ($1 + \frac{1}α$)-robust (competitiveness under terrible predictions), where $α\in (0, 1]$ is a hyper-parameter representing the level of distrust in the predictions. We also study the impact of mispredictions on the competitive ratio of the proposed algorithm and adapt it to achieve a bounded robustness while retaining its consistency. We further establish a lower bound of $\frac{3}{2}$ on the consistency of any deterministic learning-augmented algorithm. Experimental evaluations are carried out to evaluate our algorithms using real data access traces.