See, I feel silly calling myself a "software engineer" - it sounds like "sanitation engineer" or "domestic engineer" to me. I always say programmer or software developer.
No, "Engineer" (as a proper noun) is protected as a synonym for "professional engineer" (common noun phrase). The common noun "engineer" is not protected in any States.
Texas at least would appear to be different or at least the licensing board would like you to think so. "The terms "engineer" or "professional engineer" can only be used by persons who are currently licensed." [1]
That said, in my experience all manner of technical professionals (and even not so professionals) in Texas do routinely call themselves engineers whether they're supposed to or not.