The freshwater content (FWC) of the Arctic Ocean is intimately linked to the stratification—a physical characteristic of the Arctic Ocean with wide relevance for climate and biology. Here, we explore the relationship between atmospheric circulation and Arctic FWC across 12 different Coupled Model Intercomparison Project Phase 5 control run simulations. Using multiple lagged regression, we seek to isolate the linear response of Arctic FWC to a step change in the strength of the Arctic Oscillation (AO), as well as the second and third orthogonal modes of SLP variability over the Arctic domain. There is broad agreement amongst models that a step change to a more anticyclonic AO leads to an increase in Arctic FWC, with an e-folding timescale of five to ten years. However, models differ widely in the degree to which a linear response to SLP variability can explain FWC changes. While the mean states, timescales and magnitudes of FWC variability may be broadly similar, the physical origins of variability are highly inconsistent between models. We perform a robustness test that incorporates a Monte Carlo approach, to determine which response functions are most likely to represent causal, physical relationships within the models, and which are artefacts of regression. Convolution with SLP reanalysis data shows that the four most robust response functions have some skill at reproducing observed accumulation of FWC during the late 1990s and 2000s, consistent with the idea that this change was largely wind-driven.