First, the timing. Cleopatra died in 30 BC. United states did not exist till nearly 1800 years later. So she cannot be “American.” Even such a notion was not in place at that time.
Second, her family. The Ptolemaic dynasty were Greek royalties that had arrived in Egypt following Alexander the great. Their culture remained largely Greek over the generations, and they married the members of their own families.
Third, the evidence. There are coins and statues made under her life. They depict a woman with the usual Mediterranean (Greek) appearances. Even her Roman enemies never wrote of her appearance being different than of other Greeks.
Finally, identity. In the ancient days, there were no terms such as African-American used to refer to people. These people were Greek, Egyptian, or Roman–not in the present classification.
The truth is therefore easy to understand, Cleopatra was a Greek queen who reigned in Egypt. Addressing her as an African-American confuses history and the current notions in a manner that simply does not suit.