Yes, most anesthesiologists do residency (Internship) after Medical school. Its roughly 3-8 years after you graduate from Medical School. Then you do your residency and finally you can become an anesthesiologist
An anesthesiology internship takes place after medical school and the standard four years of residency. This internship is considered specialist training, so it is usually a three year fellowship done after the four years of residency.
The ones I've read about last only about a month, but there isn't a standard for this. Your school and your state will determine the exact length. However it's done, it is a lot of work and scary, I'm told.