@Tuna,
The answer to the question depends on how one defines "scientist". Presumably a scientist should possess an earned degree in a scientific discipline.
Is that enough? If I have a bachelor's degree in physics from Podunk University but I haven't published any peer reviewed papers and I work at Burger King, am I a scientist?
Then there is the issue of whether being a scientist permits one to make authoritative pronouncements on subjects outside one's area of specialty. A chemist is a type of scientist but may not be the ideal source for information about global climatology, for example.
Only close scrutiny of Dawkins' curriculum vitae and professional experience, along with a comparison to the subjects he regularly writes about, could answer the question satisfactorily. Dawkins has a number of honorary degrees but they don't count for present purposes.
It looks like from 1962-66 he was a research assistant at Oxford, which is parenthetically marked "D. Phil. 1966" . Then an Assistant Professor of Zoology at University of California, Berkeley. Three years later Senior Research Officer at the Department of Zoology, Oxford, which lasted two or three years. Then 20 years as a lecturer in Zoology at Oxford. In 1989 he apparently earned a "D. Sc." degree at Oxford but his CV gives no details and the date is rather late in his career.