Yes, the Back-to-Africa movement, also called Black Zionism, was such a movement that saw popularity in pre-civil war times, reconstruction, and a brief revival in the 1920s.

It started up in the 19th centuries, when many free blacks in both the North and South, in response to the hostility they faced when attempting to integrate into white American society. To some people in both racial groups,the idea of free blacks immigrating to the land of their ancestors seemed an attractive solution for these tensions. The American Colonization Society was founded in 1816, with the support of both slaveholder a who wanted to prevent rebellion agitated by freedmen, as well as those who believed that slavery wasn't economically viable, as well as abolitionist groups, notably Quakers, who believed that African Americans would see better, more full lives, in Africa, as well as the more religious abolitionists hoping to reduce pagan and Muslim presence in the US. From 1821 to 1847, when Liberia became independent, the ACS helped to move over 13,000 black Americans to Liberia, and continued to send more until 1867, when it effectively ceased operations save for continued publication of it's quartlerly journal, which continued until 1919. Among the black community, the ACS had a mixed reputation, with some supporting the movement, and others condemning it as a deception of a better life to trick blacks from leaving the land of opportunity to an uncertain future in a faraway land. Nevertheless, many freedmen did go to Liberia, especially after it's independence. Some notable ACS members included presidents Jefferson, Madison, Monroe, and Lincoln.

Another pre-civil war Back-to-Africa movement led to the creation of another African nation, Sierra Leone. Paul Cuffee, a wealthy black man from Massachusetts, helped the British resettle freed slaves, who had mostly fled to Nova Scotia following the American Revolution, in what is now Sierra Leone.

After the Civil War and the emancipation of American slaves, the Back-to-Africa movement saw a revival with the end of reconstruction, and the rise of the KKK and increased lynchings, the continued segregation and discrimination they faced in both north and south made many Afro-Americans skeptical that equality could ever be achieved, and made the concept of "returning to the motherland" all the more appealing, with immigration to Africa hitting a peak in the 1890s, which is also when lynchings reached a peak. The movement began to decline again around the turn of the century, due to a number of factors, primarily the growing sense of American identity among the black community, preferring to stay home rather than move to an alien land that they had no real connection to for generations.

The movement saw it's final revival in the 1920s, under the Jamaican-born Pan-African activist Marcus Garvey. Garvey founded the Black Star Line, a company that in addition to shipping goods, was also meant to serve as transport for African Americans across the Atlantic to their ancestral lands. However, due to the poor condition of the line's ships, financial difficulties, and research by the Bureau of Investigation, the FBIs forerunner, that BSL had committed mail fraud, by advertising a ship they intended to buy, but did not own, leading to Garvey, but none of the other BSL officials, being sentenced to five years in prison followed by deportation to Jamaica.

With Garvey's arrest, BSL, which was already in debt anywhere from $630,000 to $1.2 Million, ceased to function, however, it's legacy lives on in the flag of another African country, Ghana, which depicts a lack star in the center, partly as an homage to Garvey's movement.