I use hog rings for that.This one could be twisted better but its on there I usually spin it around again on the tags so it's pointing down.
View attachment 1842091 The chicken wire waisted to the 2x4 wire
But to answer OP's question if the run is to contain chickens during the day you don't have the same concerns as you would using welded wire where they sleep. A chicken will know to back away from a critter reaching into the fence. Not so if they're roosting asleep.