Woodrats

oh wait, "woodrat"
read it as "hoodrat"

in that case

put a string on it and tie it to something

Do you know anybody with a Jack Russel or Rat Terrier? It's really fun to watch them commit genocide on a rat colony.

Saw one with a pitbull and 2 little terriers.

She would kill 2 for every 1 the 2 little dogs got.

Most effective thing is get rid of all food sources if you can. On your property that means no bird feeders, no dog poop and no fallen fruit under trees. If a nearby restaurant or grocery allows rats in the dumpsters, post a service request at 311. Check under your car hood to see if rats are nesting in your car and chewing wires. Try mint oil if you see rat droppings.

Saw a youtube video of a dude catching them with a bucket. It had food in it and the lid had a false floor that would close after they fell through. Dude had a dozen or so after one night

I tried those traps with the huge rats that I have and they just ate the bait and I only caught 2. 4 traps set over 2 weeks. Bait gone daily.

As others posted, getting rid of food sources is the first thing. I still have them around my patio even after getting rid of food. I know you didn't want poison, but the TomCat bait stations (black box, sealed except for hole where rat enters) work well. I have two dogs and they haven't messed with those boxes. I do find that the rats are still around because the poison keeps getting eaten every month or two, and I find dead rats in the yard from time to time. Otherwise, the live rat traps are the way to go, then you have to deal with disposing of the critter yourself.