The short answer
Yes — budgies adore grapes, but they're very sugary and often heavily sprayed, so keep them to a treat.
Why
Grapes are essentially water and natural sugar. They're safe and loved, but too many can cause loose droppings and contribute to weight gain. Grapes also carry a lot of pesticide residue, so washing matters.
How to feed it
Choose seedless grapes, wash them thoroughly, and cut one in half so your budgie can get to the flesh. Both green and red are fine.
How much & how often
Half a grape a couple of times a week.