Do you have to be born wicca to perform magic?

The simple answer is no, anyone can research, study, write, practice and/or perform magic (the manipulation of naturally occurring powers and energies by the hand and will of an ethical practitioner). It take time, patience, and learning, but anyone can do it.

A Clarification

Nobody is born a Wiccan. When a baby is born to a Wiccan family, they hold a Wiccaning ceremony to bring the child to the Wiccan community.

The acceptance into the Wiccan Ritual Circle is not until the "Initiation" into the tradition, or coven.

You don't even has to be initiated to Wicca to practice Magic or Witchcraft, anyone can do if they learn and practice and has the ability to control their powers.

A Pagan Answer

Not all practitioners of magic are Wiccan. Although Wicca is the most commonly known Pagan spiritual path it is a long way from the only one.

Many people practice magic, either as part of their personal spiritual path or as part of their non-spiritual studies.

Conversely, not all Wiccans practice magic.

That said, in most of the pagan paths I know of a child is not "brought into" the spiritual path until he/she is an adult. We introduce the child to the gods in general, asking them all to watch over him/her until such time as he/she makes the decision themselves.