In short, yes you can!
If you are new to exercise or have only tried little amounts of resistance training, then YES, bodyweight training will definitely help YOU build muscle.
For those more used to weight training/resistance training, it’ll prove tougher. It is possible, but you’ll have to do the right exercises and gradually make them more difficult over time.
The problem with bodyweight exercises for muscle building is that it’s often very difficult to create enough tension, especially in your lower body, to stimulate growth. Muscles like the glutes and the lats (some of your biggest muscles) are harder to challenge with just bodyweight exercises, especially when you don't have access to pull up bars etc. too!
By simply just adding more reps to bodyweight exercises, you'll most likely end up just improving your muscular endurance and not size.
In order to put on muscle using bodyweight exercises, you have to make basic exercises a lot more difficult, for example squats can become a one-legged squat or simple press ups can be advanced to a one-arm push-up. Then pull-ups progress to one arm pull ups.
Two other great ways to help build muscle with bodyweight only exercises are:
Improvise and use everyday items to add additional weight. I.e. bottles of waters, bags, etc.
Slow down your reps to increase the time under tension (TUT).
It can take time to build up to, so get your basics down first!