Following commercial deployment of SG, 6G research has attracted attention from both academia and industry. 6G will continue to support what has been promised in SG, and in addition to that, it will bring new opportunities for economic growth by offering high precision services such as immersive services and metaverse. 6G will be much more complex than SG, and autonomous systems will be indispensable in reaching the aims of 6G networks. Autonomous systems for 6G let AI models themselves make decisions autonomously to operate the network and meet service requirements. Little or zero human intervention will be expected in the process of decision making. As many 6G services are mission-critical applications or have direct impacts on human lives, ethical responsibility and trustworthiness is a necessity of 6G autonomous systems and is also one of the key factors to ensure the success of 6G. In this article, we propose a new framework for ethically responsible and trustworthy autonomous systems for 6G by embedding an ethical platform for the responsible delivery of an AI project into the system design. In addition to the proposed framework, we also develop a closed control loop to reduce human intervention in the process of decision making. A case study on edge offloading is provided to show the practicality of the proposed framework. At the end of the article, we provide a list of research challenges and open issues that would be useful in guiding further research in this area.