We present observations of the known edge-on debris disk around HIP 79977 (HD 146897, F star in Upper Sco, 123 pc), taken with the ZIMPOL differential polarimeter of the SPHERE instrument in the Very Broad Band filter ($lambda_c=735$ nm, $Deltalambda=290$ nm) with a spatial resolution of about 25 mas. We measure the polarization flux along and perpendicular to the disk spine of the highly inclined disk for projected separations between 0.2 (25 AU) and 1.6 (200 AU) and investigate the diagnostic potential of such data with model simulations. The polarized flux contrast ratio for the disk is $F_{pol}/F_ast= (5.5 pm 0.9) 10^{-4}$. The surface brightness reaches a maximum of 16.2 mag arcsec$^{-2}$ at a separation of $0.2-0.5$ along the disk spine with a maximum surface brightness contrast of 7.64 mag arcsec$^{-2}$. The polarized flux has a minimum near the star $<0.2$ because no or only little polarization is produced by forward or backward scattering in the disk section lying in front of or behind the star. The data are modeled as a circular dust belt with an inclination $i=85(pm 1.5)^circ$ and a radius between $r_0$ = 60 AU and 90 AU. The radial density dependence is described by $(r/r_0)^{alpha}$ with a steep power law index $alpha=5$ inside $r_0$ and a more shallow index $alpha=-2.5$ outside $r_0$. The scattering asymmetry factor lies between $g$ = 0.2 and 0.6 adopting a scattering angle-dependence for the fractional polarization as for Rayleigh scattering. Our data are qualitatively very similar to the case of AU Mic and they confirm that edge-on debris disks have a polarization minimum at a position near the star and a maximum near the projected separation of the main debris belt. The comparison of the polarized flux contrast ratio $F_{pol}/F_{ast}$ with the fractional infrared excess provides strong constraints on the scattering albedo of the dust.
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