We have studied the variability of spectral lines caused by rotation of the primary in the binary star theta(1) Ori C and measured the radial velocities of the components. It turtles out that only the spectral lines of He II lambda 4199, 4541, 5411 and Si III lambda 4552, 4567, 4574 of the primary and secondary components, respectively, are suitable for studying the orbital motion. In addition, it is necessary to reach the signal-to-noise ratio S/N >= 300 for reliable measurements of radial velocities in the spectral region where the Si III lines are located. Variability of the radial velocities has been studied for both components using new spectroscopic data obtained during periastron passage of the system as well as previous observations. The combined 3D orbit of the system has been constructed to derive precise orbital parameters using interferometric observations together with spectral data.