The first orbital solution for the spectroscopic pair in the multiple star system sigma Scorpii, determined from measurements with the Sydney University Stellar Interferometer, is presented. The primary component is of beta Cephei variable type and has been one of the most intensively studied examples of its class. The orbital solution, when combined with radial velocity results found in the literature, yields a distance of 174(-18)(+23) pc, which is consistent with, but more accurate than the Hipparcos value. For the primary component we determine 18.4 +/not superset of 5.4 M-circle dot, -4.12 +/not superset of 0.34 mag and 12.7 +/not superset of 1.8 R-circle dot for the mass, absolute visual magnitude and radius, respectively. A B1 dwarf spectral type and luminosity class for the secondary is proposed from the mass determination of 11.9 +/not superset of 3.1 M-circle dot and the estimated system age of 10 Myr.