Broadband, efficient and fast conversion of light to electricity is crucial for sensing and clean energy. The bulk photovoltaic effect (BPVE) is a second-order nonlinear optical effect that intrinsically converts light into electrical current. Here, we demonstrate a large mid-infrared BPVE in microscopic devices of the Weyl semimetal TaAs. This discovery results from combining recent developments in Weyl semimetals, focused-ion beam fabrication and theoretical works suggesting a connection between BPVE and topology. We also present a detailed symmetry analysis that allows us to separate the shift current response from photothermal effects. The magnitude and wavelength range of the assigned shift current may impact optical detectors, clean energy and topology, and demonstrate the utility of Weyl semimetals for practical applications.