Multi-domain aspect-based sentiment analysis (ABSA) seeks to capture fine-grained sentiment across diverse domains. While existing research narrowly focuses on single-domain applications constrained by methodological limitations and data scarcity, the reality is that sentiment naturally traverses multiple domains. Although large language models (LLMs) offer a promising solution for ABSA, it is difficult to integrate effectively with established techniques, including graph-based models and linguistics, because modifying their internal architecture is not easy. To alleviate this problem, we propose a novel framework, Feature-aware In-context Learning for Multi-domain ABSA (FaiMA). The core insight of FaiMA is to utilize in-context learning (ICL) as a feature-aware mechanism that facilitates adaptive learning in multi-domain ABSA tasks. Specifically, we employ a multi-head graph attention network as a text encoder optimized by heuristic rules for linguistic, domain, and sentiment features. Through contrastive learning, we optimize sentence representations by focusing on these diverse features. Additionally, we construct an efficient indexing mechanism, allowing FaiMA to stably retrieve highly relevant examples across multiple dimensions for any given input. To evaluate the efficacy of FaiMA, we build the first multi-domain ABSA benchmark dataset. Extensive experimental results demonstrate that FaiMA achieves significant performance improvements in multiple domains compared to baselines, increasing F1 by 2.07% on average. Source code and data sets are available at https://github.com/SupritYoung/FaiMA.