We introduce a new arbitrary-shaped text detection approach named ReLaText by formulating text detection as a visual relationship detection problem. To demonstrate the effectiveness of this new formulation, we start from using a "link" relationship to address the challenging text-line grouping problem firstly. The key idea is to decompose text detection into two subproblems, namely detection of text primitives and prediction of link relationships between nearby text primitive pairs. Specifically, an anchor-free region proposal network based text detector is first used to detect text primitives of different scales from different feature maps of a feature pyramid network, from which a text primitive graph is constructed by linking each pair of nearby text primitives detected from a same feature map with an edge. Then, a Graph Convolutional Network (GCN) based link relationship prediction module is used to prune wrongly-linked edges in the text primitive graph to generate a number of disjoint subgraphs, each representing a detected text instance. As GCN can effectively leverage context information to improve link prediction accuracy, our GCN based text-line grouping approach can achieve better text detection accuracy than previous text-line grouping methods, especially when dealing with text instances with large inter-character or very small inter-line spacings. Consequently, the proposed ReLaText achieves state-of-the-art performance on five public text detection benchmarks, namely RCTW-17, MSRA-TD500, Total-Text, CTW1500 and DAST1500.