kroaches need water too !the answer is unlikely the water that comes out of the rim ports comes from your tank.when you flush you pull open a flapper valve which dumps the stored water from the tank.Its then refilled with fresh water till a float valve shut it off.maybe he like's the brown stuff you've left on the rim?

Hi,

I just had a cockroach under the toilet rim of my toilet, I flushed it and the water that came out of the rim flushed it out. Is it possible for cockroaches to get in through the toilet rim? It wasn't very clean (for some reason I get a lot of brown grime that comes from the rim and down into the toilet and I havent cleaned it for a while), it rained a lot this afternoon so I am guessing it tried to get in because of that.

Thanks