Coming from a previously skinny guy (went from 150 to 163 lbs at 6'1 and planning to go to 168-170):
Eat more fat and protein (meat, fish, eggs) and hit the gym for short high intensity strength training (do compound exercises like weighted squats, deadlifts, reverse rows, pull-ups, bench press, bar dips, overhead press). You'll gain muscle mass.
You don't have to go extreme low-carb, you can still eat 100-150 grams a day, sometimes even extending it to 150-200 grams of carbs on days with high physical activity. This is not low-carb, this is normal carb. The standard american diet is high carb, not normal.
Just make sure the carbs come from veggies and starch and a bit of fruits. Avoid grains, they are nutritionally inferior foods that human beings never ate in their natural habitat. ALL grain foods are processed foods, you can't eat grain raw and digest it, you have to throw it in a mill and grind it to pieces, than make a processed food out of it. Eating that type of food is not in alignment with how nature intended us to eat. Get the bulk of your calories from meat, eggs, fish and other high fat foods such as avocado, olives and coconut.