Re-orientation of Arabidopsis seedlings induces a rapid, asymmetric release of the growth regulator auxin from gravity-sensing columella cells at the root apex. The resulting lateral auxin gradient is hypothesized to drive differential cell expansion in elongation-zone tissues. We mapped those root tissues that function to transport or respond to auxin during a gravitropic response. Targeted expression of the auxin influx facilitator AUX1 demonstrated that root gravitropism requires auxin to be transported via the lateral root cap to all elongating epidermal cells. A three-dimensional model of the root elongation zone predicted that AUX1 causes the majority of auxin to accumulate in the epidermis. Selectively disrupting the auxin responsiveness of expanding epidermal cells by expressing a mutant form of the AUX/IAA17 protein, axr3-1, abolished root gravitropism. We conclude that gravitropic curvature in Arabidopsis roots is primarily driven by the differential expansion of epidermal cells in response to an influx-carrier-dependent auxin gradient.