Only pasteurized honey, rarely, in tiny amounts. Raw honey can carry botulism spores, and either way it's pure sugar.
Keeper's noteHoney's main legitimate use is as a vanishingly thin glue for medication or a once-in-a-blue-moon treat stick. Check labels: many 'honey treat' bird products are sugar bombs best left on the shelf.
What to watch out for with honey
Raw honey can harbor Clostridium botulinum spores — the same reason it's banned for human infants — and avian botulism is devastating. Pasteurized honey removes that risk but remains concentrated sugar with no nutritional case for a parrot.
How to serve it
Pasteurized only — never raw or 'natural unfiltered' honey.