There is no "height" restriction for employment as a pilot. That's because height as most people measure it (standing height) is pretty meaningless for considering whether you fit in a given cockpit.
However, there are a whole range of anthropometric requirements for potential aircrew. These are specific to the functional requirements of operating an aircraft. Sitting height ensures you aren't going to bang your head on the canopy or not be able to see over the coming. Buttock to knee length makes sure you won't leave your kneecaps behind if you eject. Functional reach checks you will be able to reach all of the flight deck controls while strapped in.
Most cockpits are designed to be accessible for the 2nd to the 98th percentiles of the population. So most people should fit. However, a basic tenet of anthropometry is that there is no such thing as an average person. It is almost impossible to find someone who is in the second or third quantiles for all of the 10 main anthropetric measurements.
For example, I'm a pretty 'average' 5 foot 11 inches. But I am long in the back and have short legs. Accordingly, I am only a borderline pass on sitting height for fast jets.
Anthro measurements need specialist equipment and a trained operator. AFCO will not be able to advise you.
All that can be said here is that if the closer you are to 'average' height and build, the less likely it is that you will have a problem. But as others have said, there are very tall and very short people who get in and relatively 'average' people that don't.