I have heard claims that Muslims travelled with Columbus and pbs.org makes the following claims:

"When the first Muslims came to the land that would become the United States is unclear. Many historians claim that the earliest Muslims came from the Senegambian region of Africa in the early 14th century. It is believed they were Moors, expelled from Spain, who made their way to the Caribbean and possibly to the Gulf of Mexico.

When Columbus made his journey to the United States, it is said he took with him a book written by Portuguese Muslims who had navigated their way to the New World in the 12th century.

Others claim there were Muslims, most notably a man named Istafan, who accompanied the Spanish as a guide to the New World in the early 16th century in their conquest of what would become Arizona and New Mexico.

What is clear is the make up of the first real wave of Muslims in the United States: African slaves of whom 10 to 15 percent were said to be Muslims. Maintaining their religion was difficult and many were forcibly converted to Christianity. Any effort to practice Islam, and keep the traditional clothing and names alive had to be done in secret. There was an enclave of African-Americans on the Georgia coast that managed to maintain their faith until the early part of the 20th century."

http://www.pbs.org/opb/historydetectives/feature/islam-in-america/