Recent LLMs increasingly rely on explicit reasoning mechanisms such as Chain-of-Thought, but these reasoning traces also create a new attack surface for inference-time backdoors that steer the model toward malicious reasoning paths without modifying its parameters. Such attacks can remain linguistically coherent, making them difficult to detect with surface-, consistency-, or confidence-based signals. We propose STAR, a lightweight detection framework that compares input-conditioned token probabilities with prior-only reasoning probabilities. STAR measures token-level prior-posterior amplification and applies CUSUM to identify persistent anomalies in the generated reasoning process. Experiments across four LLMs (8B-70B), five reasoning benchmarks, and three inference-time backdoor attacks show that STAR achieves strong detection performance, with an average AUROC of 0.980, and substantially lower TFLOPs than high-overhead baselines such as Onion. STAR also remains effective under top-k logit access and the evaluated burn-in-aware adaptive attacks, while exposing a trade-off between evasion attempts and attack success.