I think I see your faces as you think: at last there is someone who will tell me if you can permanently cure anxiety or not.
Okay. It's like this: it depends.
Sorry for the preamble (which is not the best for an anxious person), come straight to the point and then go into some things.
First of all, there is only one type of anxiety disorders and there is no single cause for anxiety.
The answers depend largely on the type of care that is undertaken, and how long the anxiety disorder is part of the life of the individual. In addition we must also consider anxiety-inducing components are part of the personality and other related disorders.
So what you need is a diagnosis. So that's the official response. An informal answer would be: yes, if not part of your personality. Please note that in this case you can lower the level of your anxiety until it becomes a background invisible and embark on a path to healing or if self-care, you can control it virtually forever without the use of drugs.
If the anxiety stems from something more specific like a trauma that could be called mild and in the absence of other more serious diseases, then we say that with a suitable path to healing, in principle, should to solve the problem, even permanently. Subject, of course, exceptions to the rule and your motivation to change.