Aims: NGC 4631 is an interacting galaxy which exhibits one of the largest gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and polarization properties of its disk and halo emission with new radio continuum data. Methods: Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C and D array configurations, and at L-band (1.57 GHz) in the B, C, and D array configurations. The Rotation Measure Synthesis algorithm was utilized to derive the polarization properties. Results: We detected linearly polarized emission at C-band and L-band. The magnetic field in the halo is characterized by strong vertical components above and below the central region of the galaxy. The magnetic field in the disk is only clearly seen in the eastern side of NGC 4631, where it is parallel to the plane of the major axis of the galaxy. We detected for the first time a large-scale, smooth Faraday depth pattern in a halo of an external spiral galaxy, which implies the existence of a regular (coherent) magnetic field. A quasi-periodic pattern in Faraday depth with field reversals was found in the northern halo of the galaxy. Conclusions: The field reversals in the northern halo of NGC 4631, together with the observed polarization angles, indicate giant magnetic ropes with alternating directions. To our knowledge, this is the first time such reversals are observed in an external galaxy. Reduced polarized intensity images are also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/632/A11