The short answer
Yes — apple is a safe and popular treat for budgies, as long as you remove every seed first.
Why
Apple flesh is hydrating and most budgies love it. The danger is the seeds (pips): they contain amygdalin, which releases cyanide when crushed. Because a budgie is so tiny, even a few seeds can be harmful, so they must always be removed.
How to feed it
Wash the apple (they're heavily sprayed, so organic is ideal), cut a thin slice, and carefully remove the core and all seeds. The skin is fine to leave on. Clip the piece to the cage bars or offer it in a dish.
How much & how often
A couple of small pieces, 2–3 times a week. Apple is sugary, so treat it as a snack rather than a daily food.