Cooked rice is a tricky one: yes, it’ll rot down pretty quickly but in the meantime, it is a haven for bacteria (which could cause other problems for your compost heap). Plus, if it has come into contact with any oils, fats, meats or other flavourings, it might attract unwanted vermin. Some people have composted it for years without problems but others decide the little benefit you’d get from cooked rice isn’t worth the risk.
On the other hand, worms in wormeries love it – they typically “process” it before it becomes a problem.
So it’s a definite maybe: yes, add it to a wormery and possibly to an enclosed or well-established compost bin, but maybe leave it out of a basic, slow-composting heap for the time being.