like everyone before me said, you can't be born with the power, it takes years to become one, and if you do, you must be registered under the ministry of magic, or else you are illegal like Padfoot (sirius) Prongs (James) and Wormtail (peter.)
It says in The Prisoner of Azkaban that it took James, Sirius and Peter from their 2nd year, to their 5th year to fully become an animagus.
Also, i would like to say, that if i was an animagus, i would be a fox or if underwater, a seahorse.
McGonagal, Sirius, James, and Peter are all animagus'