We present a total time series of high signal-to-noise, high-resolution spectra of the SiIII lambda 4552.6, lambda 4567.8 and lambda 4574.8 Å lines of the fast-rotating, spectroscopic binary and beta Cephei star kappa Scorpii. Among this data set is a sample of 422 spectra of intensive monitoring during eight subsequent nights in July 1997. We find variability of the line profiles on two time-scales: a variation of several months as a result of the orbital motion and rapid variations of a few hours, which are explained in terms of non-radial pulsation modes. From the total dataset, covering a time span of 9 years, we derive for the first time the orbital parameters of kappa Scorpii and find an orbital period of 195 days. The complex patterns on the grayscale representations of the residual SiIII lambda 4552.6 Å profiles with respect to the average profile point towards more than one (non-axisymmetric) pulsation mode. A frequency analysis of the three normalised velocity moments confirms the main period of 4.80 hours and the second period of 4.93 hours, which were previously derived from photometric data. We attempt an identification of the pulsation modes by means of the moment method and line-profile fitting and find that kappa Scorpii pulsates in a main prograde sectoral mode of degree 1 or 2 and in an additional tesseral mode for which l = 5, m = 1 are the most likely wavenumbers. In the variations of the line profiles we find indications for the presence of additional pulsation modes. Based on observations obtained at ESO with the CAT/CES, La Silla, Chile.