In a small saucepan, bring the rice, 1 cup water and 1/4 teaspoon salt to a boil. Lower the heat, cover and simmer until the water is absorbed, about 17 minutes. Fluff with a fork and let cool.
Meanwhile, fill another saucepan with salted water. Add the carrot, bring to a boil and cook for 2 minutes. Using a slotted spoon, transfer to a bowl; toss with 2 tablespoons olive oil, the vinegar and oregano. Season with salt and pepper.
In the same saucepan, blanch the corn in the boiling water for 3 minutes; transfer to the bowl with the carrot. Add the peas to the boiling water and cook for 1 minute. Transfer to the bowl.
Add the rice, cubed celery, chopped celery leaves and onion to the bowl, season with salt and pepper, drizzle with the remaining 2 tablespoons olive oil and toss.