  We prove an effective version of a result due to Einsiedler, Mozes, Shah and
Shapira who established the equidistribution of primitive rational points on
expanding horospheres in the space of unimodular lattices in at least $3$
dimensions. Their proof uses techniques from homogeneous dynamics and relies in
particular on measure-classification theorems -- an approach which does not
lend itself to effective bounds. We implement a strategy based on spectral
theory, Fourier analysis and Weil's bound for Kloosterman sums in order to
quantify the rate of equidistribution for a specific horospherical subgroup in
any dimension. We apply our result to provide a rate of convergence to the
limiting distribution for the appropriately rescaled diameters of random
circulant graphs.
