The 1880s was the start of the post-chanties era -- when landsmen were becoming aware of chanties while at the same time their demise was being lamented. Evidently, "Rio Grande" had become well-known enough that it could be referred to in a parody version, as in this college songster.

1887        Hills, W.H., ed. _Students' Songs_. Thirteenth ed. Boston: Rand Avery.

On pg 34 it includes a non-nautical version called "The Annex Maid," copyrighted 1881 by the author. The chorus is, "And I come from the Rio Grande."