The fundamental frequency (F0) represents pitch in speech that determines prosodic characteristics of speech and is needed in various tasks for speech analysis and synthesis. Despite decades of research on this topic, F0 estimation at low signal-to-noise ratios (SNRs) in unexpected noise conditions remains difficult. This work proposes a new approach to noise robust F0 estimation using a recurrent neural network (RNN) trained in a supervised manner. Recent studies employ deep neural networks (DNNs) for F0 tracking as a frame-by-frame classification task into quantised frequency states but we propose waveform-to-sinusoid regression instead to achieve both noise robustness and accurate estimation with increased frequency resolution. Experimental results with PTDB-TUG corpus contaminated by additive noise (NOISEX-92) demonstrate that the proposed method improves gross pitch error (GPE) rate and fine pitch error (FPE) by more than 35 % at SNRs between -10 dB and +10 dB compared with well-known noise robust F0 tracker, PEFAC. Furthermore, the proposed method also outperforms state-of-the-art DNN-based approaches by more than 15 % in terms of both FPE and GPE rate over the preceding SNR range.