Multi-modal relation extraction (MRE) requires the integration of multi-modal information to identify relationships between entities. Although fine-grained correlations between visual objects and textual words have the potential to improve cross-modal interaction, they are typically modeled implicitly and hindered by the modality gap. This paper introduces a novel method called relational Graph-Bridged cross-modal InTeraction (GBIT). GBIT aims to model fine-grained cross-modal correlations into the interaction process explicitly. This is achieved by constructing a fine-grained cross-modal relational graph, which acts as a bridge for effective cross-modal interaction in multiple layers. Within GBIT, a gated interaction strategy and an adaptive integration module are proposed for irrelevance-filtered information exchange and final information collation. Through extensive experiments on the benchmark MRE, we demonstrate the superiority of our proposed method for MRE.