Respiratory rate (RR) is a clinical sign representing ventilation. An abnormal change in RR is often the first sign of health deterioration as the body attempts to maintain oxygen delivery to its tissues. There has been a growing interest in remotely monitoring of RR in everyday settings which has made photoplethysmography (PPG) monitoring wearable devices an attractive choice. PPG signals are useful sources for RR extraction due to the presence of respiration-induced modulations in them. The existing PPG-based RR estimation methods mainly rely on hand-crafted rules and manual parameters tuning. An end-to-end deep learning approach was recently proposed, however, despite its automatic nature, the performance of this method is not ideal using the real world data. In this paper, we present an end-to-end and accurate pipeline for RR estimation using Cycle Generative Adversarial Networks (CycleGAN) to reconstruct respiratory signals from raw PPG signals. Our results demonstrate a higher RR estimation accuracy of up to 2$times$ (mean absolute error of 1.9$pm$0.3 using five fold cross validation) compared to the state-of-th-art using a identical publicly available dataset. Our results suggest that CycleGAN can be a valuable method for RR estimation from raw PPG signals.