This blog post will answer the question: can bearded dragons eat grapes? Bearded dragons can eat grapes but they must be only fed as an occasional treat. Grapes are high in fibre and calcium which is great for lizards.
Keep in mind the size of the grape you are feeding to your bearded dragon, You may need to cut them into small pieces depending on the size of your bearded dragon. This is more important if your bearded dragon is a hatchling/Juvi.
Grapes are high in moisture, Oxalates and sugar which could cause harm to your bearded dragon if given in large amounts.