There must be a broker employed by the company, but either you can be the broker or you must hire one (there must be a "broker of record" filed with the state). I know many owners of property management companies who hire a broker rather than getting a license themselves. However, I don't recommend that. Better to have the expertise of a broker yourself if you are going to manage your company effectively.
"CHAPTER 3. REAL ESTATE REGULATIONS, Article 1. Scope of Regulation", Sections 10130/10131(b)
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I am not a lawyer; however, my personal opinion is that you do need a Broker License.