yes you can do it with the help of exercise.
No, you don't want to get fatter. You might want to get more muscle, but fat isn't healthy. Being thin is extremely healthy, so you have to weight vanity against health, but if you're emaciated, just eat more of what you're already eating and don't burn any more of it off. Exercise is important for the health of your internal organs, so yes, you should exercise. Resistance training will add muscle, which will make you less thin without making you fat.