COVID-19 has prompted unprecedented government action around the world. We introduce the Oxford COVID-19 Government Response Tracker (OxCGRT), a dataset that addresses the need for continuously updated, readily usable and comparable information on policy measures. From 1 January 2020, the data capture government policies related to closure and containment, health and economic policy for more than 180 countries, plus several countries' subnational jurisdictions. Policy responses are recorded on ordinal or continuous scales for 19 policy areas, capturing variation in degree of response. We present two motivating applications of the data, highlighting patterns in the timing of policy adoption and subsequent policy easing and reimposition, and illustrating how the data can be combined with behavioural and epidemiological indicators. This database enables researchers and policymakers to explore the empirical effects of policy responses on the spread of COVID-19 cases and deaths, as well as on economic and social welfare.