Drainage canals associated with logging and agriculture dry out organic soils in tropical peatlands, thereby threatening the viability of long-term carbon stores due to increased emissions from decomposition, fire, and fluvial transport. In Southeast Asian peatlands, which have experienced decades of land use change, the exact extent and spatial distribution of drainage canals are unknown. This has prevented regional-scale investigation of the relationships between drainage, land use, and carbon emissions. Here, we create the first regional map of drainage canals using high resolution satellite imagery and a convolutional neural network. We find that drainage is widespread-occurring in at least 65% of peatlands and across all land use types. Although previous estimates of peatland carbon emissions have relied on land use as a proxy for drainage, our maps show substantial variation in drainage density within land use types. Subsidence rates are 3.2 times larger in intensively drained areas than in non-drained areas, highlighting the central role of drainage in mediating peat subsidence. Accounting for drainage canals was found to improve a subsidence prediction model by 30%, suggesting that canals contain information about subsidence not captured by land use alone. Thus, our data set can be used to improve subsidence and associated carbon emissions predictions in peatlands, and to target areas for hydrologic restoration.