The first human can be traced back to Africa. African-American is simply a term used to denote the fact that many Black Americans have ancestors from Africa. In fact, scientifically speaking all races have ancestors that orginated in Africa if you want to get technical. http://www.selamta.net/Lucy.htm
None of this has anything to do with religion. There is nothing remotely similar to the two.
I am going to answer this question by eliminating religion from the discussion. Many African Americans are Christian and there are growing numbers of African American Muslims in the United States. For that simple fact, I don't think you could consider African Americans a religion. In addition, most people chose their religion, whereas I cannot chose to be African American.
If they are any of these things, they are a race. We must keep in mind that race is only a social construct, though.
They aren't a religion because they can belong to many different religions. They are not an ethnic group because African Americans can be Spanish-speaking, can come from Africa, or can come from ancestors who have been in North America since the 1600s. This leaves only race. To some extent, African Americans look different from the rest of us. This is the only thing that they truly have in common with one another. Therefore, they can only be called a race if we have to call them one of these things.