Cross-modal retrieval (CMR) aims to establish interaction between different modalities, among which supervised CMR is emerging due to its flexibility in learning semantic category discrimination. Despite the remarkable performance of previous supervised CMR methods, much of their success can be attributed to the well-annotated data. However, even for unimodal data, precise annotation is expensive and time-consuming, and it becomes more challenging with the multimodal scenario. In practice, massive multimodal data are collected from the Internet with coarse annotation, which inevitably introduces noisy labels. Training with such misleading labels would bring two key challenges -- enforcing the multimodal samples to \emph{align incorrect semantics} and \emph{widen the heterogeneous gap}, resulting in poor retrieval performance. To tackle these challenges, this work proposes UOT-RCL, a Unified framework based on Optimal Transport (OT) for Robust Cross-modal Retrieval. First, we propose a semantic alignment based on partial OT to progressively correct the noisy labels, where a novel cross-modal consistent cost function is designed to blend different modalities and provide precise transport cost. Second, to narrow the discrepancy in multi-modal data, an OT-based relation alignment is proposed to infer the semantic-level cross-modal matching. Both of these two components leverage the inherent correlation among multi-modal data to facilitate effective cost function. The experiments on three widely-used cross-modal retrieval datasets demonstrate that our UOT-RCL surpasses the state-of-the-art approaches and significantly improves the robustness against noisy labels.