In Antarctica, Global Positioning System (GPS) vertical time series exhibit non-linear signals over a wide range of temporal scales. To explain these non-linearities, a number of hypotheses have been proposed, among them the short-term rapid solid Earth response to contemporaneous ice mass change. Here we use GPS vertical time series to reveal the solid Earth response to variations in surface mass balance (SMB) in the Southern Antarctic Peninsula (SAP). At four locations in the SAP we show that interannual variations of SMB anomalies cause measurable elastic deformation. We use regional climate model SMB products to calculate the induced displacement assuming a perfectly elastic Earth. Our results show a reduction of the misfit when fitting a linear trend to GPS time series corrected for the elastic response to SMB variations. Our results imply that, for a better understanding of the glacial isostatic adjustment signal in Antarctica, SMB variability must be considered.