Graph Anomaly Detection (GAD) has demonstrated great effectiveness in identifying unusual patterns within graph-structured data. However, while labeled anomalies are often scarce in emerging applications, existing supervised GAD approaches are either ineffective or not applicable when moved across graph domains due to distribution shifts and heterogeneous feature spaces. To address these challenges, we present GADT3, a novel test-time training framework for cross-domain GAD. GADT3 combines supervised and self-supervised learning during training while adapting to a new domain during test time using only self-supervised learning by leveraging a homophily-based affinity score that captures domain-invariant properties of anomalies. Our framework introduces four key innovations to cross-domain GAD: an effective self-supervision scheme, an attention-based mechanism that dynamically learns edge importance weights during message passing, domain-specific encoders for handling heterogeneous features, and class-aware regularization to address imbalance. Experiments across multiple cross-domain settings demonstrate that GADT3 significantly outperforms existing approaches, achieving average improvements of over 8.2\% in AUROC and AUPRC compared to the best competing model.