A rooster is a low-level monster that is very similar to a chicken, and indeed they are found together.
The attackable ones are members-only, but there is a rooster in the farm near Falador standing on the top of the box in the chicken pen even on a free-to-play world. It looks exactly like the Evil Chicken, a former random event and a boss monster in the quest Recipe for Disaster. However, that one cannot be attacked. Roosters may be killed for the bird slayer task, they give 7 Slayer experience per kill.