There have been increasing concerns about Artificial Intelligence (AI) due to its unfathomable potential power. To make AI address ethical challenges and shun undesirable outcomes, researchers proposed to develop socially responsible AI (SRAI). One of these approaches is causal learning (CL). We survey state-of-the-art methods of CL for SRAI. We begin by examining the seven CL tools to enhance the social responsibility of AI, then review how existing works have succeeded using these tools to tackle issues in developing SRAI such as fairness. The goal of this survey is to bring forefront the potentials and promises of CL for SRAI.