This paper reports a novel approach that uses transistor aging in an integrated circuit (IC) to detect hardware Trojans. When a transistor is aged, it results in delays along several paths of the IC. This increase in delay results in timing violations that reveal as timing errors at the output of the IC during its operation. We present experiments using aging-aware standard cell libraries to illustrate the usefulness of the technique in detecting hardware Trojans. Combining IC aging with over-clocking produces a pattern of bit errors at the IC output by the induced timing violations. We use machine learning to learn the bit error distribution at the output of a clean IC. We differentiate the divergence in the pattern of bit errors because of a Trojan in the IC from this baseline distribution. We simulate the golden IC and show robustness to IC-to-IC manufacturing variations. The approach is effective and can detect a Trojan even if we place it far off the critical paths. Results on benchmarks from the Trust-hub show a detection accuracy of $\geq$99%.