The earliest example I have is Jose Antonio Bolcof of Russia, who became a Mexican about 1833. Who beat him?
cf. Who was the first foreigner to be naturalized as a Mexican citizen?: several Texans got in before Bolcof.
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I found these two while researching your other question.
"In 1814, John Gilroy, a Scottish sailor on an English ship, was left in Monterey because of illness. He was baptized and naturalized, then married a daughter of a well-known ranchero and became a ranchero himself. The present-day town of Gilroy bears his name.
In 1822, William E.P. Hartnell who represented the British firm John Begg & Co. signed a three-year contract with the missions for their production of hides and tallow. As the first foreign businessman, Hartnell soon converted to Catholicism, married into a ranchero family, and acquired Rancho Patrocinio del Alisal."
Looks like being 1828. Hittell's "History of California" says:
On April 14, 1828, the Mexican congress passed a naturalization law.... In June, 1829, [Governor] Echeandia issued a circular in reference to the subject; and almost immediately afterwards a number of applications for naturalization were presented. William G. Dana, an American, had already in July, 1828, upon making the necessary declaration, been allowed to marry an "hija del pais" or daughter of the country and become naturalized....
Abel Stearns emigrated to Mexico in 1826 and naturalized in 1828. In 1829 he moved out to Monterey, California, and he eventually settled in Pueblo de los Ángeles, which would become the Los Angeles that we know today.
The RootsWeb biography says:
One year after his marriage, he purchased the 28,000-acre Rancho Los Alamitos, near present day Long Beach and Seal Beach, to use as a summer home. As a trader who settled in Los Angeles, Stearns had become one of the area's wealthiest citizens and the largest landowner in Southern California.
The Online Archive of California says:
Stearns was in Mexico City 1826-1829