There were tons of Blue Eagle merchandise produced during 1933, especially -- any kind of a gimcrack that could have the logo impressed upon it was manfuactured and sold. It became something of a scandal when it was discovered that a lot of this dime-store paraphernalia was being stamped out in factories that did not, in fact, comply with NRA codes.
I'm going to guess that it's a novelty ring made for high-school or college kids, and the "37" is meant to represent a class year. The Class of '37 would have been freshmen when the NRA was at the peak of its popularity.
Saw a partial display case of similar rings, minus the year. They were originally under-the-counter merchandise in a small-town general store; when I saw them they were in the basement, along with almost a hundred years of other flotsam and jetsam of unsold merchandise. They were packed in one of those slotted ring displays, like you see at flea markets. Nothing special, as I recall the original price was <$1.
No, I didn't buy one. The only ones remaining wouldn't even fit me as a pinky ring.