An autonomous household robot passed a self-awareness test in 2015, proving that the cognitive capabilities of robots are heading towards those of humans. While this is a milestone in AI, it raises questions about legal implications. If robots are progressively developing cognition, it is important to discuss whether they are entitled to justice pursuant to conventional notions of human rights. This paper offers a comprehensive discussion of this complex question through cross-disciplinary scholarly sources from computer science, ethics, and law. The computer science perspective dissects hardware and software of robots to unveil whether human behavior can be efficiently replicated. The ethics perspective utilizes insights from robot ethics scholars to help decide whether robots can act morally enough to be endowed with human rights. The legal perspective provides an in-depth discussion of human rights with an emphasis on eligibility. The article concludes with recommendations including open research issues.