The generation of photocurrent in an ideal two-dimensional Dirac spectrum is symmetry forbidden. In sharp contrast, a three-dimensional Weyl semimetal can generically support significant photocurrent due to the combination of inversion symmetry breaking and finite tilts of the Weyl spectrum. To realize this photocurrent, a noncentrosymmetric Weyl semimetal is coupled to a pair of electrodes and illuminated with circularly polarized light without any voltage applied to the Weyl semimetal. The wavelength of the incident light can range over tens of microns and can be adjusted by doping the Weyl semimetal to change its chemical potential.