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The Brazilian Amazon plays a central role in regulating regional and global climate, storing carbon, and sustaining biodiversity, while simultaneously serving as an evolving agricultural frontier shaped by economic incentives, forest conservation policies, and environmental constraints. Recent literature highlights climate variability, particularly drought, as a critical yet understudied driver of forest loss in the Brazilian Amazon. This paper aims to answer the following policy-relevant questions: (1) How do drought shocks affect deforestation in the Brazilian Amazon? (2) Does this effect vary systematically across farm types with different economic vulnerabilities? (3) What do these patterns imply for the social cost of unmitigated climate shocks and for the design of integrated climate adaptation and forest conservation policy? Using the high-resolution (0.25°, ~28km) daily root zone soil moisture (RZSM) data from NASA's Global Land Data Assimilation System, we construct standardized bottom-decile historical RZSM deficits for the Legal Amazon in Brazil. We aggregate these daily RZSM deficits into annual and seasonal cummulative RZSM deficits as our drought measures at the municipality-RZSM grid level. Using the high-resolution (30m by 30m) MapBiomas annual land cover data, we count deforested pixels relative to the base year of 2000 and aggregate them at the municipality-RZSM grid level. We estimate a dynamic panel fixed-effects model for a sample period of 2005-2019, regressing deforestation on annual RZSM deficits, controlling for lagged forest stock, exogenous crop and cattle prices, and lagged municipality- and region-specific policy interventions. We find that increases in RZSM deficits lead to significantly higher deforestation within the same year, with no statistically detectable within-year feedback from deforestation to local moisture flow once we condition on prior forest stock. The effect is substantially larger in municipalities with a higher prevalence of family farms. Consistent this heterogeneity, these municipalities experience significantly larger increases in forest-related environmental fines during periods of soil moisture deficits, suggesting greater engagement in illegal deforestation activities. We provide evidence on the underlying mechanism by showing that drought reduces agricultural output more sharply in these municipalities, indicating heightened economic distress. Moreover, we find that improved access to credit partially mitigates drought-induced deforestation, pointing to a potential role for policy interventions in alleviating environmentally harmful coping responses. Finally, we quantify the economic welfare cost of drought-induced forest loss by combining our estimated deforestation responses with standard biomass carbon estimates for the Amazon (approximately 150–200 tCO₂ per hectare) and the U.S. Interagency Working Group Social Cost of Carbon ($51–$190/tCO₂, 2020 USD). This yields a monetized estimate of the additional carbon damage attributable to drought shocks, 22.5-111.6 million USD per year (with damages 1–3 times larger during severe drought years), suggesting a sizable social benefit of policies that prevent income-stress-driven deforestation in the Brazilian Amazon.