We measure the small-scale (comoving separation ) two-point correlation function of quasars using a sample of 26 spectroscopically confirmed binary quasars at 0.6 < z < 2.2 from the Sloan Digital Sky Survey Quasar Lens Search (SQLS). Thanks to careful candidate selections and extensive follow-up observations of the SQLS, which are aimed at constructing a complete quasar lens sample, our sample of binary quasars is also expected to be nearly complete within a specified range of angular separations and redshifts. The measured small-scale correlation function rises steeply towards smaller scales, which is consistent with earlier studies based on incomplete or smaller binary quasar samples. We find that the quasar correlation function can be fitted by a power law reasonably well over 4 orders of magnitude, with the best-fitting slope of ξ(r) ∝ r−1.92. We interpret the measured correlation function within the framework of the halo occupation distribution (HOD). We propose a simple model that assumes a constant fraction of quasars that appear as satellites in dark matter haloes, and find that measured small-scale clustering signals constrain the satellite fraction to fsat=0.054+0.017−0.016 for a singular isothermal sphere number density profile of satellites. We note that the HOD modelling appears to underpredict clustering signals at the smallest separations of rp∼ 10 h−1 kpc unless we assume very steep number density profiles (such as a Navarro–Frenk–White profile with the concentration parameter cvir≳30), which may be suggestive of enhanced quasar activities by direct interactions.