  In the present paper we investigate the limiting behaviour of short
incomplete Gauss sums at random argument as the number of terms goes to
infinity. We prove that the limit distribution is given by the distribution of
theta sums and differs from the limit law for long Gauss sums studied by the
author and Marklof. The key ingredient in the proof is an equidistribution
theorem for rational points on horocycles in the metaplectic cover of SL(2,R).
