Segregation and racism in general was definitely used as anti-American propaganda in the Soviet Union. It was sufficiently common to the point that in the late Soviet Union, the phrase "and you are lynching negroes" or variations thereof became a punchline to jokes, where somebody would ask a question about the state of the Soviet Union in comparison to America and the Soviet person would reply with that stock phrase. It was not originally a laughing matter for the Soviets, though. Wikipedia has helpfully hosted a scan of a Soviet propaganda poster depicting an African American being lynched, dating to 1930.
Here is a previous answer from this board by u/kieslowskifan. Although the subject is not strictly identical, instead asking "what were the views of African Americans about the Soviet Union?", there is a very substantial overlap between this answer and the question you're asking here.
Institutional racism in the United States did not only serve as internal propaganda to lessen the appeal of American modernity and economic prosperity, but also helped Communism appeal to people internationally. Communism was egalitarian (in theory) and the USSR rejected biological racism. The answer linked above divides campaigns of anti-racist propaganda into three eras - the initial period of 1919 through to the 1920's, a renewal in the 1930's, and then the cold-war era. In each case, the exact motivation for a rewewal of emphasis on American racism was different, but you should go read that post for the full details.
On occasion, though, the Soviet authorities sought to exploit the racial divide in America on a more direct basis. In The Sword and the Shield: The Mitrokhin Archive and the Secret History of the KGB, the author explains that "active measures" (a broad term encompassing anything from publishing propaganda to assassination) were undertaken to discredit MLK while he was alive, the KGB believing that he was potentially going to defuse a race-war they hoped would break out in America. Propaganda was published portraying Martin as an "Uncle Tom" and attempting to discredit efforts at mediation of the civil rights movement made by the American government. After his assassination, the strategy was switched towards one whereby he was portrayed as a martyr, but much for the same reason - it was an attempt to stoke the flames of underlying tensions in the United States.
Hi! you might be interested in some of these earlier posts
How did (or did) the USSR use the US's Civil Rights movement and issues like Jim Crow as propaganda?
How did the Soviet Union seem to feel about Martin Luther King Jr. during the Civil Rights Movement?
Did the Soviet Union have a "bite-sized" refutation of Capitalism?
Did fear of Communism play a significant role in the granting of civil rights to American blacks?
Is there any evidence of Soviet/Communist involvement in the black civil rights movement?