In Dragon Age Origins can you be a dragon

If you have it on PC, there is a mod that lets you turn into the high dragon and the arch demon, along with many other creatures, like golems, blight wolves, and many more

However, if you play it on the PS3 then no you can not turn into any type of dragon.
Or any other creature for that matter. Unless you are a mage and know shape shifting.
Or you can be a Ranger which allows you to turn into animals such as a bear, a wolf, and the swarm of insects.