There was a lot of discussion about what we now call "racism" in
the late 1800s and early 1900s but I agree with others that the term
"racism" does not seem to have been used yet.  It also does not
show up in searches of the Making of America site at the Univ. of
Michigan.  Here are a few examples of the use of "race prejudice,"
"race pride," and "lynching spirit" I found in documents in my Anti-
Imperialism in the U.S. web:

"When, right here at home, the laws are ignored and men are
lynched, almost daily, because of race prejudice, he must be an
optimist indeed who believes that Americans will be less prejudiced
3,000 miles away from home.... Maybe there is some alchemy in
the Pacific breezes which will neutralize the race pride for which we
have become infamous; but if I were a Filipino I should not care to
put faith in it."
--Herbert S. Bigelow, "Jose Rizal, Filipino Patriot" (1899)

"I cannot believe I am mistaken in supposing that the lynching
spirit has shown itself conspicuously bold and self-congratulatory
in the northern and western as well as in the southern states of the
union, since it became possible for the hoarse and brutal muse of
Rudyard Kipling to sing the nation's policy and purpose [in "The
White Man's Burden"]."
-- Quincy Ewing, "An Effect of the Conquest of the Philippines"
(1901)

"The spirit which slaughters brown men in Jolo is the spirit which
lynches black men in the South. When such crimes go
unpunished, far more when the men who commit them are praised
and rewarded, the youth of the country is taught an evil lesson.
Race prejudice is strengthened and the love of justice, the corner-
stone of free institutions, is weakened."
--Moorfield Storey, "The Moro Massacre" (1906).

That was the same Moro Massacre that Twain commented upon in
his autobiography.  Storey was president of the Anti-Imperialist
League in 1906 and four years later became the first president of
the NAACP.  Bigelow and Ewing were also among the country's
most outspoken opponents of "racism" during that period.

Jim Zwick