The photoplethysmogram (PPG) obtained from pulse oximetry shows the local changes of blood volume in tissues. Respiration induces variation in the PPG baseline due to the variation in venous blood return during each breathing cycle. We have proposed an algorithm based on the synchrosqueezing transform (SST) to estimate instantaneous respiratory rate (IRR) from the PPG. The SST is a combination of wavelet analysis and a reallocation method which aims to sharpen the time-frequency representation of the signal and can provide an accurate estimation of instantaneous frequency. In this application, the SST was applied to the PPG and IRR was detected as the predominant ridge in the respiratory band (0.1 Hz - 1 Hz) in the SST plane. The algorithm was tested against the Capnobase benchmark dataset that contains PPG, capnography, and expert labelled reference respiratory rate from 42 subjects. The IRR estimation accuracy was assessed using the root mean square (RMS) error and Bland-Altman plot. The median RMS error was 0.39 breaths/min for all subjects which ranged from the lowest error of 0.18 breaths/min to the highest error of 13.86 breaths/min. A Bland-Altman plot showed an agreement between the IRR obtained from PPG and reference respiratory rate with a bias of -0.32 and limits agreement of -7.72 to 7.07. Extracting IRR from PPG expands the functionality of pulse oximeters and provides additional diagnostic power to this non-invasive monitoring tool.