The solid Earth strains in response to the gravitational pull from the Moon, Sun, and other planetary bodies. Measuring the flexure of geologic material in response to these Earth tides provides information about the geomechanical properties of rock and sediment. Such measurements are particularly useful for understanding dilation of faults and fractures in competent rock. A new approach to measuring earth tides using fiber optic distributed acoustic sensing (DAS) is presented here. DAS was originally designed to record acoustic vibration through the measurement of dynamic strain on a fiber optic cable. Here, laboratory experiments demonstrate that oscillating strain can be measured with DAS in the microHertz frequency range, corresponding to half-day (M2) lunar tidal cycles. Although the magnitude of strain measured in the laboratory is larger than what would be expected due to earth tides, a clear signal at half-day period was extracted from the data. With the increased signal-to-noise expected from quiet field applications and improvements to DAS using engineered fiber, earth tides could potentially be measured in deep boreholes with DAS. Because of the distributed nature of the sensor (0.25 m measurement interval over kilometers), fractures could be simultaneously located and evaluated. Such measurements would provide valuable information regarding the placement and stiffness of open fractures in bedrock. Characterization of bedrock fractures is an important goal for multiple subsurface operations such as petroleum extraction, geothermal energy recovery, and geologic carbon sequestration.