Yes, you can eat stir-fry rice with a spoon if you prefer to do so or if that's the utensil available to you. While it is more common to eat rice with chopsticks in some Asian cultures or with a fork in Western cultures, using a spoon is perfectly acceptable.
Using a spoon can be particularly helpful if the rice is mixed with a variety of vegetables, meats, or sauces in a stir-fry, as it allows you to scoop up a combination of flavors in each bite. Ultimately, how you choose to eat stir-fry rice is a matter of personal preference, so feel free to use a spoon or any other utensil that makes the dining experience enjoyable for you.