Most sisters belong to Roman Catholic orders – an order is a group of women who live in the spirit (or charism) of a particular founder, and have their own rules for living. The rules (or Mercy Constitutions) of most orders are approved by the Church. So, yes, you have to be Catholic to be a Catholic sister. (There are other kinds of nuns, e.g., Anglican nuns and Buddhist nuns.)
Being Catholic means that you have received all the sacraments of initiation: baptism, confirmation, and first communion. It means a regular practice of your faith, including attending Mass and being active in your parish community. It also is good to make retreats and/or to meet with a spiritual director. These help to strengthen your understanding and practice of your faith.
You can become a sister if you are a new Catholic, but you will be asked to wait for three years after your initiation so that you have time to adjust to your new faith experience before taking another serious step in your life.