Observational evidence suggests that river inflows to the Arctic Ocean have increased over the last 30 years. Continued increases have the potential to alter the freshwater balance in the Arctic and North Atlantic Oceans and hence the thermohaline circulation. Simulations with a macroscale hydrological model and climate change scenarios derived from six climate models and two emissions scenarios suggest increases of up to 31% in river inflows to the Arctic by the 2080s under high emissions and up to 24% under lower emissions, although there are large differences between climate models. Uncertainty analysis suggests low sensitivity to model form and parameterization but higher sensitivity to the input data used to drive the model. The addition of up to 0.048 sverdrup (Sv, 106 m3 s-1) is a large proportion of the 0.06--0.15 Sv of additional freshwater that may trigger thermohaline collapse. Changes in the spatial distribution of inflows to the Arctic Ocean may influence circulation patterns within the ocean.