I recently dealt with the same problem using a live catch cage trap from Bunnings. The rat ignored the peanut butter I tried first but I bought the special rat attractant and had the little bastard within a week.

I had other kill traps out (nooski and electronic) but they didn't work. He triggered the nooski a couple of times but got away unharmed.

Just stick the trap along your fence where you've seen him and wait.