We propose FACTER, a fairness-aware framework for LLM-based recommendation systems that integrates conformal prediction with dynamic prompt engineering. By introducing an adaptive semantic variance threshold and a violation-triggered mechanism, FACTER automatically tightens fairness constraints whenever biased patterns emerge. We further develop an adversarial prompt generator that leverages historical violations to reduce repeated demographic biases without retraining the LLM. Empirical results on MovieLens and Amazon show that FACTER substantially reduces fairness violations (up to 95.5%) while maintaining strong recommendation accuracy, revealing semantic variance as a potent proxy of bias.