One who has taken refuge and follows the teachings of the Buddha.
Many who read about the Dharma and understands it well but has not
taken refuge eventually due to even deeper understanding, takes
refuge.
After all, a Buddhist is one who follows the way of Buddha. Just as
Christian is one who follows the way of Christ. Thus taking refuge
is 1st step in following the path of Buddhism.
But anyone can call themself a buddhist. They can even call
themself God if they want.