Yes you can cook rice in a frying pan or skillet.
When cooking rice in a frying pan or skillet just add a little rice and then add some water to cover the rice.
The rice will cook just fine in the frying pan or skillet and just make sure you stir the rice around often enough to avoid it sticking to the pan.
The rice will absorb the water as it cooks and once the rice is soft then the rice is done.
Rice is best cooked in a pot so that you can add more rice and avoid the water boiling over more easier but if all you have is a skillet or frying pan then that will work too.
You just have to cook less rice at one time when cooking the rice in the skillet.
Or you could put the rice in a microwave safe bowl and then add water to the bowl and cook the rice for 10 to 15 minutes or until the rice is soft.