Using daily data from August 9, 2015, to July 7, 2020, this study examines the effects of economic policy uncertainty (EPU) on the returns of four cryptocurrencies: Bitcoin, Ethereum, Litecoin, and Ripple. To this end, two new measures of EPU (Twitter-based economic uncertainty and Twitter-based market uncertainty) are considered. A Granger causality test using the recursive evolving window approach shows a significant causality between the Twitter-based EPU measures and the BTC/USD exchange rate from October 2016 to July 2017. Moreover, a significant causality was noted from the EPU measures to the ETH/USD exchange rate from June 2019 to February 2020 and from the EPU measures to the XRP/USD exchange rate from January 2020 to February 2020. The Twitter-based EPU measures primarily positively affect the returns of the related cryptocurrencies during these periods. These results are robust to different measures of Twitter-based EPU and different econometric techniques. Potential implications, including the COVID-19 era, are also discussed.