I've hunted and shot a lot of crows in my life, and I have taken them with 22LR, 222's, 223's, 12ga, and even a few with a 110gr 30-06 load. Usually when riding and scouting farm fields and pastures, I used my 222 Rem in a 700 BDL with either 50gr TNT loads or some of my hand swaged frangible 17gr bullets for zero ricochet around cattle.
When using an electronic caller and/or decoys, a good 12ga load with 6 or 7 1/2 shot in either modified or full choke. For real short term excitement, wing one and then step on his wing to hold him down and let him scream - Things can become Alfred Hitchcock's "The Birds" very fast.