We propose the Soft Graph Transformer (SGT), a soft-input-soft-output neural architecture designed for MIMO detection. While Maximum Likelihood (ML) detection achieves optimal accuracy, its exponential complexity makes it infeasible in large systems, and conventional message-passing algorithms rely on asymptotic assumptions that often fail in finite dimensions. Recent Transformer-based detectors show strong performance but typically overlook the MIMO factor graph structure and cannot exploit prior soft information. SGT addresses these limitations by combining self-attention, which encodes contextual dependencies within symbol and constraint subgraphs, with graph-aware cross-attention, which performs structured message passing across subgraphs. Its soft-input interface allows the integration of auxiliary priors, producing effective soft outputs while maintaining computational efficiency. Experiments demonstrate that SGT achieves near-ML performance and offers a flexible and interpretable framework for receiver systems that leverage soft priors.