We cross-match high-precision astrometric data from Gaia DR2 with accurate multiband photometry from the Dark Energy Survey (DES) DR1 to confidently measure proper motions for nine stellar streams in the DES footprint: Aliqa Uma, ATLAS, Chenab, Elqui, Indus, Jhelum, Phoenix, Tucana III, and Turranburra. We determine low-confidence proper-motion measurements for four additional stellar streams: Ravi, Wambelong, Willka Yaku, and Turbio. We find evidence for a misalignment between stream tracks and the systemic proper motion of streams that may suggest a systematic gravitational influence from the Large Magellanic Cloud (LMC). These proper motions, when combined with radial velocity measurements, will allow for detailed orbit modeling that can be used to constrain properties of the LMC and its effect on nearby streams, as well as global properties of the Milky Way's gravitational potential.