Yes and no. It depends on the type of relationship detailed in the collective bargaining agreement between the union and your employer. Even if you have good reasons for refusing to join, you may not have any choice, unless you live in a state that has right-to-work provisions.
Your agreement with the union may provide for one of the following:
(1) an open shop: there is no need to join or pay dues.
(2) an agency shop: you don't have to join, but you will have to pay the same dues as if you were a member.
(3) union shop: you do not have to be a union member prior to taking your job, but once accepted, you must join the union after a specified period of time.