That would be the destroyer USS Ward, and the midget sub sank from flooding from a 4" shell hole in her conning tower. The
sub was found by H.U.R.L. in 2002 using the DSV's Pisces IV and V.
You can look up sinkings by boat
here. As Torplexed said, it looks like USS Swordfish gets credit for the first ship sinking by a US submarine (read her 1st war patrol report
here). It's interesting though that the first official (ie. JANAC seal of approval) sinking was likely not, in fact, the first ship sunk by the Swordfish.