With the continuing growth in various research domains such as Artificial Intelligence (AI), Machine Learning (ML), Big Data Analytics (BDA), and Cloud Computing (CC), the Internet of Things (IoT) has become a popular technology nowadays. It provides a virtual interaction between physical objects and the cyber world over the Internet without human intervention. The IoT devices are embedded with sensors, software, or some other useful technologies for connecting, sharing, and exchanging data with other devices. Among recent technologies impacting human lives, Radio Frequency IDentification (RFID) has become a core identification technology that can be integrated into the IoT environments which connect billions of things or objects. However, an RFID system has two major issues: (i) an adversary can tamper or intercept the sensitive information of the RFID tags, which may cause forgery and privacy problems, and (ii) RFID tags have limited computational power capability which makes it challenging to use current security solutions. To deal with these issues, we propose an anonymous and reliable ultralightweight RFID-enabled authentication scheme (namely AnonR²AS) for IoT systems in a cloud computing environment. AnonR²AS integrates bitwise exclusive-OR, left–right rotations, and ultralightweight half-flip operation, to reduce computational overheads on tag. The AnonR²AS provides stronger security (by preventing several attacks) and improves performance concerning low computational, communication, and storage costs. Also, it preserves information privacy and tags untraceability property by using Vaudenay privacy model. The Scyther simulation tool verification has been performed for its formal security analysis. The performance analysis ensures our AnonR²AS scheme is preferable for low-cost RFID systems.