Computed tomography (CT) restoration methods often use a single network for low-dose CT (LDCT), sparse-view CT (SVCT), and metal artifact reduction (MAR), despite the distinct physics of these degradations. We propose AgentCT, a vision-language agent that identifies the degradation and routes images to task-specific restoration models. A LoRA-adapted Qwen3-VL-4B controller predicts degradation type and severity, selects a specialist, and reassesses the restored image. The LDCT specialist uses an image-domain diffusion model, whereas the SVCT and MAR specialists combine projection-domain correction, data consistency, differentiable filtered back-projection, and image refinement. We evaluated the controller and specialists separately on patient-disjoint Mayo 2020 abdominal CT data across three severity levels for each degradation. The controller achieved 95.7% accuracy for degradation type and 93.9% for severity, with a 100% JSON parse rate. Using ground-truth degradation labels for routing, AgentCT achieved an overall PSNR/SSIM of 46.18 dB/0.984, compared with 44.93 dB/0.976 for AMIR and 44.29 dB/0.979 for TAMP, and attained the highest PSNR in all nine settings. For SVCT, its dual-domain specialist achieved 46.04 dB with 4.2 million parameters, compared with 44.43 dB for single-task AMIR and 43.57 dB for all-in-one AMIR with 23.5 million parameters. These results support degradation-specific CT restoration with controller-based model selection; evaluation under automatic routing and on independent clinical data remains necessary. Code is available at https://github.com/hao1635/AgentCT.

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