Yes — fresh thyme is a safe, aromatic herb that's fine for parrots in normal fresh-leaf amounts.
Keeper's noteA fresh sprig in the chop or clipped to the bars. Fresh leaves only — skip thyme essential oil.
Why thyme is good for parrots
Fresh thyme is non-toxic and carries antioxidant and antimicrobial compounds. Like other culinary herbs, it's offered as fresh leaves in small amounts the bird self-limits. Avoid concentrated thyme oil, which is far too strong.