Yes.

President Chester A. Arthur banned Chinese immigrants for 10 years with the Chinese Exclusion Act in 1882. It was renewed in part in 1892 by the Geary Act, which put additional restrictions on Chinese residents. They were required to register and obtain a certificate of residence, without which they could be deported. Things stayed roughly the same for Chinese immigration for the next few decades. That was until the Magnuson Act 0f 1943, which allowed for some Chinese immigration as well as some Chinese already residing in the country to become naturalized citizens, but it still maintained the ban on property and business ownership.

During World War II, President Franklin D. Roosevelt limited the amount of German Jews that could immigrate here, which was capped at 26,000 annually. He primarily based this limitation on the fears that Nazi spies could be hiding amongst them.

In 1903, the Anarchist Exclusion Act signed by President Theodore Roosevelt banned anarchists and others deemed to be political extremists from entering the US. President William McKinley had been fatally shot in 1901 by Leon Czolgosz, an American anarchist who was the son of Polish immigrants. The act, officially known as the Immigration Act of 1903, banned those deemed as anarchists, as well as those with epilepsy, beggars and importers of prostitutes.

The Internal Security Act of 1950, known also as the McCarran Act, was put in place to deport any immigrants believed to be members of the Communist Party. Members of communist organizations were also not allowed to become citizens. President Harry Truman opposed the law, and vetoed it. However, Congress overrode his veto and passed it into law. Some sections of the act were ruled unconstitutional by the Supreme Court in 1993, but some parts of the act still stand.

In response to the 1979 Iranian hostage crisis, in April 1980 President Jimmy Carter severed diplomatic relations with and imposed sanctions on Iran, as well as banning Iranians from entering the country.

While not strictly a ban on immigrants based on country, in 1987 President Ronald Reagan imposed a ban on HIV positive persons trying to enter the United States. The law was unfortunately based on the racist, homophobic and xenophobic sentiments of the era, as well as the false assumption that HIV could be spread by physical contact. President George W. Bush started the procedures to lift this ban during his time in office, and President Barack Obama lifted the ban completely in 2009.

Hi there -- just wanted to drop in a reminder note that this question is fine here, but that we specifically don't want to talk about modern politics. Anything up to 1997 (inclusive) is fine though! The relevant rule can be found here. Thanks!