No. You can choose in any given moment to eat or not to eat, but you can't simply choose to have an eating disorder.
Anorexia nervosa arises out of complex factors. It is not something that shows up like the common cold, and it's not a disorder that a person can "create" by force of will.
It's not uncommon for a person who wants to lose weight to say something like, "I wish that I could get anorexia; then I could be thinner." This person is unaware of how anorexia can appear, and she (or he) is also unaware of the major health risks that go with the disorder.
In other words, even if you could catch anorexia like a virus, you definitely wouldn't want to do it.

