Using data on four USD-pegged stablecoins and 27 fiat currencies, this paper documents spillovers from stablecoin-based foreign exchange (FX) to traditional FX markets. We document a gap between the cost of acquiring dollars via stablecoins and via the spot FX market (parity deviations). To establish a causal link between stablecoin flows and FX markets, we use a granular instrumental variable that exploits idiosyncratic shocks to stablecoin net inflows in other currencies. Our estimates indicate that a 1% exogenous increase in net stablecoin inflows raises parity deviations by 40 basis points, depreciates the local currency, and widens the dollar premium in synthetic funding markets (covered interest parity (CIP) deviations). A model of constrained arbitrage rationalizes these findings and provides structural foundations for the identification strategy. Counterfactual simulations show that halving cross-market frictions would attenuate CIP spillovers by roughly one-half and cut exchange rate effects by nearly one-third. A dynamic extension that closely matches the empirical impulse responses shows that spillovers grow disproportionately when intermediaries suffer losses, as depleted capital reduces their capacity to absorb further shocks. Our results establish stablecoins as an emerging segment of global currency markets with direct implications for financial stability.