No. The Church acknowledges the marriages of non-Catholics as valid. To marry such a person without the marriage being declared null by the Catholic Church is to marry someone who is still married. That is adultery and a mortal sin. Besides, such a marriage could not take place in a Catholic Church. So the Catholic would have gotten married outside of the Catholic Church—also a mortal sin.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.