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A key objective of the Perseverance rover mission is to acquire samples of Martian rocks for future return to Earth. Eventual laboratory analyses of these samples would address key questions about the evolution of the Martian climate, interior, and habitability. Many such investigations would benefit greatly from samples of Martian bedrock that are oriented in absolute Martian geographic coordinates. However, the Mars 2020 mission was designed without a requirement for orienting the samples. Here we describe a methodology that we developed for orienting rover drill cores in the Martian geographic frame and its application to Perseverance's first 20 rock samples. To orient the cores, three angles were measured: the azimuth and hade of the core pointing vector (i.e., vector oriented along the core axis) and the core roll (i.e., the solid body angle of rotation around the pointing vector). We estimated the core pointing vector from the attitude of the rover's Coring Drill during drilling. To orient the core roll, we used oriented images of asymmetric markings on the bedrock surface acquired with the rover's Wide Angle Topographic Sensor for Operations and eNgineering (WATSON) camera. For most samples, these markings were in the form of natural features on the outcrop, while for four samples they were artificial ablation pits produced by the rover's SuperCam laser. These cores are the first geographically‐oriented (<2.7° 3σ total uncertainty) bedrock samples from another planetary body. This will enable a diversity of paleomagnetic, sedimentological, igneous, tectonic, and astrobiological studies on the returned samples. Plain Language Summary: The central goal of the Perseverance rover is to drill rock samples that can be brought back to Earth. Future laboratory studies of these samples could tell us about the history of Mars' climate, its interior structure and whether it was once habitable. These studies would greatly benefit from information about how the rock samples were oriented relative to Martian geographic coordinates. Here we show how we developed a technique to orient cores drilled by the rover and applied it to Perseverance's first 20 rock samples. Like all methods for orienting three‐dimensional objects, this required measuring three angles which are analogous to the pitch, yaw, and roll of a boat. We measured the the first two angles using the known orientation of the rover arm during drilling. We measured the third angle using rover photographs of markings on the rock face prior to drilling. These markings were either natural features on the outcrop or, for rock faces with no clear natural markings, an artificial L‐shaped pattern of pits produced by the rover's laser. These cores are the first geographically‐oriented samples of bedrock from another planet. This will enable a diversity of geological, geophysical, and paleontological studies on the samples in Earth laboratories. Key Points: The Perseverance rover has acquired drill cores of Martian igneous and sedimentary bedrock for future potential return to EarthUsing rover engineering data, we have oriented all rock cores in Martian geographic coordinates to better than 2.7° uncertaintyOrientation enables future studies of the paleodirections associated with Martian magmatic, sedimentary, tectonic, and magnetic processes [ABSTRACT FROM AUTHOR]