Here's what the state of Texas says about it:
Graduates of all public universities recognized by the American Association of Colleges and Universities who have a degree from an ABET engineering program have the right to disclose any college degrees received and use the title "Graduate Engineer" on stationery, business cards, and personal communications of any character. A graduate engineer who is employed by a registered firm and who is supervised by a licensed professional engineer may use the term "engineer". Refer to the Texas Engineering Practice Act, Section 1001.406.
But it's pretty rare for a non-licensed engineer to get in trouble for claiming to be an engineer especially if they're degreed.
I have seen some building maintenance guys with engineer in their title and I really wanted to call them out on it since they're not degreed, licensed, or even know what engineers really do. But I try really hard to not be a *****.
For the record, I passed the test so I get to say I'm an engineer
