If by The Water is Wide you mean members of the song-family that contain that particular verse, then it won't have travelled to the US with Irish emigrants, as it appears to be a uniquely English variant (though I am of course ready to proved wrong on this). Sharp found it in the South of England; the well-known and much-recorded tune came from Mrs. Caroline Cox at High Ham, Somerset, in August 1905. The only variant beginning with those words listed in the Roud Folksong Index from outside England is a recording of Almeda Riddle from the 1970s: I don't know where she got it.
The Traditional Ballad Index mentions three examples that might perhaps be American:
Peggy Seeger, American Favorite Ballads: Tunes and Songs as sung by Pete Seeger (1961), p. 77, "The Water Is Wide" (1 text, 1 tune). I don't know if the book names the traditional source, if any, but Pete Seeger certainly didn't restrict himself to American songs!
Irwin Silber, Folksinger's Wordbook (1973), p. 145, "Waillie"; p. 163, "The Water Is Wide" (2 texts). The editors of the TBI comment: This book gives no source information at all about the songs contained, and at least some seem to have been edited. Useless for your purposes, then.
The most likely vector of transmission for this particular form of the song would be Cecil Sharp's book, One Hundred English Folksongs, which was published in the USA by the Oliver Ditson Company of Boston in 1916, and which contained Mrs. Cox' set, titled (because of its perceived relationship to the Scottish song) O Waly Waly. The folksong revival of the 1950s and thereafter will also have spread it around quite a lot, during which process the details of its provenance will often have been forgotten, ignored or misrepresented.
Of course, other members of the song family, lacking the Water is Wide part, were in America earlier on; Sharp got a two-verse fragment in the Appalachians in 1916, but didn't publish it, and a few others have turned up since. I would imagine that they mostly derived from Scottish forms, but I haven't seen the texts.