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.