We present high-resolution spectropolarimetric observations of the spectroscopic binary χ Dra. Spectral lines in the spectrum of the main component χ DraA show variable Zeeman displacement, which confirms earlier suggestions about the presence of a weak magnetic field on the surface of this star. Within about 2 yr of time base of our observations, the longitudinal component B_L of the magnetic field exhibits variation from -11.5 ± 2.5 to +11.1 ± 2.1G with a period of about 23 d. Considering the rotational velocity of χ Dra A in the literature and that newly measured in this work, this variability may be explained by the stellar rotation under the assumption that the magnetic field is globally stable. Our new measurements of the radial velocities (RV) in high-resolution I-spectra of χ DraA refined the orbital parameters and reveal persistent deviations of RVs from the orbital curve.We suspect that these deviations may be due to the influence of local magnetically generated spots, pulsations, or a Jupiter-size planet orbiting the system.