A riff of the term "golden shackle" meaning a wedding band, usually but not exclusively when worn by a man.
To "shackle cruise" is to search a person's ring finger to see if they are either wearing a wedding band, or have the tell-tale impression on their finger that a wedding band is supposed to be there.
Can be done by a woman or man.
"See that hot guy at the bar buying everybody drinks? He's really hot!"
"Yeah, I just shackle cruised him when I went to the bathroom. Let's put it this way, there's going to be a very pissed off wife when that credit card statement comes in."
"Wow, that guy on the weight bench over there is HOT. Wonder if he's gay?"
"I just shackle cruised him and unless he's from a very progressive state, you're out of luck on this one."