NO. It is not necessary for an officer to read you your rights in order to arrest you. Your 5th Amendment right to remain silent (or not to incriminate yourself) and additional right to an attorney are generally refered to as your 'Miranda Rights' (based upon an Arizona case that went to the United States Supreme Court in 1966).

An officer is only required to read you your rights if you are in custody and he is interrogating you (asking you questions.) A failure to advise a suspect of his or her rights can result in the state not being able to use the person's statements against him or her in court.