We present the design and scientific motivation for Arcus, an X-ray grating spectrometer mission to be deployed on the International Space Station. This mission will observe structure formation at and beyond the edges of clusters and galaxies, feedback from supermassive black holes, the structure of the interstellar medium and the formation and evolution of stars. The mission requirements will be R>2500 and >600 cm2 of effective area at the crucial O VII and O VIII lines, values similar to the goals of the IXO X-ray Grating Spectrometer. The full bandpass will range from 8-52Å (0.25-1.5 keV), with an overall minimum resolution of 1300 and effective area >150 cm2. We will use the silicon pore optics developed at cosine Research and proposed for ESA's Athena mission, paired with off-plane gratings being developed at the University of Iowa and combined with MIT/Lincoln Labs CCDs. This mission achieves key science goals of the New Worlds, New Horizons Decadal survey while making effective use of the International Space Station (ISS).