Yes — turnip root and especially its greens are safe and nutritious for parrots, raw or cooked.
Keeper's noteDon't discard the greens — they're the most nutritious part. Grate or cube the root for easier eating.
Why turnip is good for parrots
Turnips are non-toxic root vegetables with vitamin C and fiber, and turnip greens are a calcium- and vitamin-rich leafy green that often outshines the root nutritionally. Both raw and cooked are fine.