'Ranche turns up as a variant spelling and examples in the OED. I hadn't thought to check there.
The first use in print is from 1810, Zebulon Pike, Sources of the Mississippi: "When we arrived at the Ranche, we soon had out a number of boys, who brought in the horse."
More from the OED: Ranch is an Anglicization of the Spanish rancho. Definitions are:
1. A hut or house in the country. (Pike's use)
2. A cattle-breeding establishment, also the persons employed or living on this.
3. Use in words such as ranchwoman, ranchhouse, ranchowner.

Can someone find an earlier definite use of ranch in the sense of a cattle operation before Bret Harte and Mark Twain used the term in the 1860s? The OED is uncertain about its use in 1831 (J. O. Pattie, personal narrative)- "At a ranch, I purchased a horse for three dollars" (whether a house, farm or cattle operation is not clear to the OED editors). In 1847, Lundy- "We set off at daybreak, and went some twenty-one miles to a ranche." The OED accepts this one as referring to a livestock operation.

Another meaning is to let land for grazing (1910 example)