The vertical root distribution of riparian vegetation plays a relevant role in soil water balance, in the partition of water fluxes into evaporation and transpiration, in the biogeochemistry of hyporheic corridors, in river morphodynamics evolution, and in bioengineering applications. The aim of this work is to assess the effect of the stochastic variability of the river level on the root distribution of phreatophytic plants. A function describing the vertical root profile has been analytically obtained by coupling a white shot noise representation of the river level variability to a description of the dynamics of root growth and decay. The root profile depends on easily-determined parameters, linked to stream dynamics, vegetation and soil characteristics. The riparian vegetation of a river characterized by a high variability turns out to have a rooting system spread over larger depths, but with shallower mean root depths. In contrast, a lower river variability determines root profiles with higher mean root depths.