  We present a new, probabilistic method for determining the systemic proper
motions of Milky Way (MW) ultra-faint satellites in the Dark Energy Survey
(DES). We utilize the superb photometry from the first public data release
(DR1) of DES to select candidate members, and cross-match them with the proper
motions from $Gaia$ DR2. We model the candidate members with a mixture model
(satellite and MW) in spatial and proper motion space. This method does not
require prior knowledge of satellite membership, and can successfully determine
the tangential motion of thirteen DES satellites. With our method we present
measurements of the following satellites: Columba~I, Eridanus~III, Grus~II,
Phoenix~II, Pictor~I, Reticulum~III, and Tucana~IV; this is the first systemic
proper motion measurement for several and the majority lack extensive
spectroscopic follow-up studies. We compare these to the predictions of Large
Magellanic Cloud satellites and to the vast polar structure. With the high
precision DES photometry we conclude that most of the newly identified member
stars are very metal-poor ([Fe/H] $\lesssim -2$) similar to other ultra-faint
dwarf galaxies, while Reticulum III is likely more metal-rich. We also find
potential members in the following satellites that might indicate their overall
proper motion: Cetus~II, Kim~2, and Horologium~II; however, due to the small
number of members in each satellite, spectroscopic follow-up observations are
necessary to determine the systemic proper motion in these satellites.
