How do I cite in APA format for an author who uses only a first name?
When there is only one name, simply use that name.
The guiding principal of citation is to give a clear and unambiguous pointer for finding the work in question and related works. Thus, when dealing with a mononym, the general APA dictum of "author's last name" (which is quite culturally narrow in any case) maps cleanly to "author's only name."
Examples can easily be found for famous ancient authors such as Plato, e.g.:
Plato. (1961). Meno (R. S. Bluck, Trans.). Cambridge, England: Cambridge University Press. (Original work published ca. 380 B.C.)
The same principles can be applied for modern mononymous authors.
According to the APA Style Blog you should cite what you see. While it does not specifically cover people/references with one name, it does cover the Dalai Lama (a single title) and Dr Suess (a pseudonym that cannot be separated). Based on the cite what you see principal, just treat the name as a last name.