The unprecedented travel bans introduced in response to the COVID-19 pandemic is a pertinent phenomenon of interest to scholars across the globe. Quantifying the timing and content of policy changes affecting travel and immigration is key to future research on the spread of SARS-CoV-2 and the socioeconomic impacts of these policies. The COVID Border Accountability Project (COBAP) provides a systematized dataset of >1000 policies, reflecting a timeline of new country-level restrictions on movement across international borders during the 2020 year. Using a 20-question survey, trained research assistants (RAs) sourced and documented for each new border policy: start and end dates, whether the closure constitutes a "complete closure" or "partial closure", which exceptions are made, which countries are banned, and which borders are closed, among other variables. In addition, the full text of each policy was included in the database. We maintain and update the data monthly. For public use, we visualize the data in an interactive map tool visualization: covidborderaccountability.org. For ongoing and future pandemic research, the dataset will be useful to policymakers, social and biomedical scientists, and public health experts alike.