Most states have some protection around advertising yourself as a "Professional Engineer" (PE) or similar term that implies you are licensed by the state to provide engineering services to the public. Only a few states apply this sort of orthodoxy to the general term "engineer", and the enforcement tends to be pretty lax.
It varies state-to-state, but in my state, I'm perfectly in my rights to call myself an engineer, since I work as an engineer for an engineering company under the 'direct supervision'* of a licensed Professional Engineer. I would be in trouble, however, if I was on my own and called myself an engineer, since I am not licensed.
*Apparently, working under the direct supervision of a licensed engineer includes the PE following my advice and taking directions from the also-not-licensed owner of the company. (The owner used to be an engineer in the Soviet Union and the PE is a good guy, but only has a few years of experience and is far less knowledgeable about the field than others in the company.)