Yes, you can represent any kind of requirement in a UML model. Create or use a metaclass named Requirement and stereotype that with <<functional>>
or <<non-functional>>
. Since there are so many different non-functional classifications you can use a tagged value to determine which kind. Now you can <<trace>>
your use case (or most likely your class design) to those requirements. It's also possible to show the realization of requirements.
Instead of using tagged values you can also simply use packages where you stuff in the single requirements. The minor drawback with this is that you need to check the context of the requirement to find out where it belongs.
NB: I have not shown the stereotype in the diagram and you are also free to use or omit stereotypes. There is quite some freedom in representing things in UML.