Not the Navy. The Marines, actually.
No doubt there were some Muslims among the African slaves brought to North America in the colonial era, but to what extent any of them passed on their Muslim beliefs to their American-born children is questionable--if there were any solid evidence for that happening I'm sure it would be quoted all the time. The conditions the slaves labored under did not lend themselves to the public practice of Islam--there were no muezzins calling out the times for prayer and probably no plantations where Muslim slaves could stop what they were doing at the appointed time and say their prayers in the direction of Mecca.
http://www.history.navy.mil/biblio/biblio4/biblio4a.htm
http://www.shsu.edu/~his_ncp/USMC1.html
No...Eagles6 was right. The Marines were 'born' in 1775. Captain Samuel Nicholas formed two battalions of Continental Marines on 10 November 1775 in Philadelphia as naval infantry.
Actions against American shipping by Barbary Coast pirates in moved Congress to pass the Naval Act of 1794 ordering the construction and manning of six frigates. The US Navy was born.
Unless I'm wrong, that's how I've always read the histories.
They may have been birthed as a result of Islam, but they soon recognized the Navy’s role when several dozen Marines drowned attempting to march across the Atlantic to Tripoli.