COVID-19 has prompted a wide range of responses from governments around the world. There is a pressing need for up-to-date policy information as these responses proliferate, and governments weigh decisions about the stringency of their policies against other concerns. We introduce the Oxford COVID-19 Government Response Tracker (OxCGRT), providing a systematic way to track the stringency of government responses to COVID-19 across countries and time. Using a novel index that combines various measures of government responses, we describe variation in government responses, explore whether rising stringency of response affects the rate of infection, and identify correlates of more or less stringent responses.