A theoretical framework for the determination of tidally induced radial-velocity variations in a component of a close binary is presented. Both the free and the forced oscillations of the component are treated as linear, isentropic perturbations of a spherically symmetric star. Resonances between dynamic tides and free oscillation modes are taken into account by means of the formalism developed by Smeyers et al. (1998). The amplitude of the tidally induced radial-velocity variations seen by the observer depends on the orbital eccentricity and on the orbital inclination. The amplitude increases with increasing orbital eccentricity and is most sensitive to the value of the orbital inclination when 20degrees less than or similar to i less than or similar to 70degrees. In the case of a 5 M-(C) ZAMS star with a 1.4 M-circle dot compact companion, it is shown that resonant dynamic tides can lead to radial-velocity variations with amplitudes large enough to be detected in observations. The shape of the tidally induced radial-velocity curves varies from very irregular for orbital periods away from any resonances with free oscillation modes to sinusoidal for orbital periods close to a resonance with a free oscillation mode. Our investigation is concluded with an application to the slowly pulsating B star HD 177863 showing the possibility of resonant excitation of a high-order second-degree g(+)-mode in this star.