The short answer

Yes — plain cooked rice is a safe, gentle food for budgies.

Why

Cooked plain rice (white or brown) is easy to digest and perfectly safe; brown rice has a bit more nutrition. The key is 'plain' — no salt, butter, oil or seasoning. (Uncooked rice is also fine for birds, contrary to the old myth, but cooked is easier to eat.)

How to feed it

Offer a small spoon of plain cooked rice, cooled to room temperature.

How much & how often

Occasionally, as part of a varied diet.