Real-world digital environments are highly diverse and dynamic. These characteristics cause agents to frequently encounter unseen environments and distribution shifts, making continual learning in such environments essential for computer-use agents (CUAs). However, a key challenge lies in obtaining high-quality and environment-grounded training data without relying on costly human annotation. In this work, we introduce ACuRL, an Autonomous Curriculum Reinforcement Learning framework that continually adapts agents to specific environments with zero human data. The agent first explores an environment to acquire initial experiences. During subsequent iterative training, a curriculum task generator leverages these experiences together with feedback from the previous iteration to synthesize new tasks tailored for the agent's current capabilities. To provide reliable reward signals, we introduce CUAJudge, a robust automatic evaluator for CUAs that achieves 93% agreement with human judgments. Empirically, our method effectively enables both intra-environment and cross-environment continual learning, yielding 3-29% absolute performance gains on the target environments without catastrophic forgetting on others. We also show that it can mitigate performance degradation under environment changes (e.g., version updates, platform migration, and resolution shifts). Further analyses show highly sparse updates (e.g., only 20% parameters), which helps explain the effective and robust adaptation.