Can tall people rock climb?
Tall and short people both have the potential to become amazing climbers. Climbing does not depend on the climbers height.
There are times when being short can be beneficial, such is in very compressed movements and positions, and there are times when being tall and having a long arm span can be very useful, such as reaching farther holds easier.
The main thing to keep in mind is your technique, and how you take advantage of your height, be it shorter or taller.