Have you ever needed a Plan B drinking buddy? You know, someone you wouldn't normally hang out with at a bar or around a keg? But in the case of not having your normal drinking mates available, you call upon this person to join you. Basically, so you don't look like some serious psycho loner drinking all by your lonesome? A Boozy Call is like a "Booty call", but the booty is replaced with booze.
"Eh, Bob's cool and all. But, he's really just a Boozy Call for me."