Obstructive Sleep Apnoea (OSA) is a disorder characterised by pauses in breathing during sleep which lead to deoxygenation. It is associated with increased risk of serious conditions including cardiovascular disease, diabetes and stroke. OSA prevalence ranges from 2-7% throughout the world, but it is estimated that up to 90% of cases are undiagnosed and untreated. OSA is usually diagnosed with a costly overnight sleep study, where a large number of physiological signals are recorded and analysed. The recent increase in adoption of smartphones has led to the proliferation of many sleep screening applications, but no existing application is based on scientific evidence. In this project we propose a novel OSA screening framework involving a pulse oximeter, a smartphone and an online server. The screening algorithms have been evaluated on a clinical database of 1007 patients and show 85.6% accuracy on the test set in identifying those diagnosed with OSA. This framework has the potential to provide a simple, cheap and widely-available modality for OSA screening, particularly in developing countries where conventional screening is limited.