Yes — a little plain, fully cooked shrimp is safe and some parrots love it, but keep it occasional and completely unseasoned.
Keeper's noteOffer a small piece of plain cooked shrimp occasionally. Skip anything from a seasoned or buttered dish — that's the usual problem with seafood scraps.
What to watch out for with shrimp
Cooked shrimp is non-toxic and a source of protein, and many parrots are enthusiastic about it. The concerns are sodium and seasoning (shrimp is often cooked with salt, garlic, or butter) and the fact that it's a rich novelty food, not a staple. Plain, cooked, and small is the rule.