A giant planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) are observed in TaP, a nonmagnetic Weyl semimetal with ultrahigh mobility. The perpendicular resistivity (i.e., the planar magnetic field applied normal to the current) far exceeds the zero-field resistivity, which thus rules out the possible origin of negative longitudinal magnetoresistance. The giant PHE and AMR are finally attributed to the large anisotropic orbital magnetoresistance that stems from the ultrahigh mobility. Furthermore, the mobility-enhanced current jetting effects are found to strongly deform the line shape of the curves, and their evolution with the changing magnetic field and temperature is also studied. Although the giant PHE and AMR suggest promising applications in spintronics, the enhanced current jetting shows the other side of the coin, which needs to be considered in future device design.