We report a tight linear relation between the HI circular velocity measured at 6 $R_{rm e}$ and the stellar velocity dispersion measured within 1 $R_{rm e}$ for a sample of 16 early-type galaxies with stellar mass between $10^{10}$ and $10^{11}$ $mathrm{M}_odot$. The key difference from previous studies is that we only use spatially resolved $v_mathrm{circ}$(HI) measurements obtained at large radius for a sizeable sample of objects. We can therefore link a kinematical tracer of the gravitational potential in the dark-matter dominated outer regions of galaxies with one in the inner regions, where baryons control the distribution of mass. We find that $v_mathrm{circ}$(HI) = 1.33 $sigma_mathrm{e}$ with an observed scatter of just 12 percent. This indicates a strong coupling between luminous and dark matter from the inner- to the outer regions of early-type galaxies, analogous to the situation in spirals and dwarf irregulars. The $v_mathrm{circ}$(HI)-$sigma_mathrm{e}$ relation is shallower than those based on $v_mathrm{circ}$ measurements obtained from stellar kinematics and modelling at smaller radius, implying that vcirc declines with radius -- as in bulge-dominated spirals. Indeed, the value of $v_mathrm{circ}$(HI) is typically 25 percent lower than the maximum $v_mathrm{circ}$ derived at $sim0.2 R_mathrm{e}$ from dynamical models. Under the assumption of power-law total density profiles $rho propto r^{-gamma}$, our data imply an average logarithmic slope $langlegammarangle=2.18pm0.03$ across the sample, with a scatter of 0.11 around this value. The average slope and scatter agree with recent results obtained from stellar kinematics alone for a different sample of early-type galaxies.
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