Is it permissible for the two parties to an engagement, who met online and whose parents refused their marriage, to utter the phrase "I marry myself to you" in order to complete the legitimate Islamic marriage?

It is not permissible to utter words of marriage without a guardian for the woman, as it is invalid, and even more invalid if it is without a guardian or witnesses. If the woman desires marriage and is suitable, she has the right to refer the matter to the Sharia (definition) judge to marry her or to order her guardian to do so if her family prevents her. However, it should be noted that choosing a spouse via the internet is fraught with risks. It is advisable to strive to convince the family to agree, otherwise, each of them should turn away from the other, and cut off all relations between them unless a valid legal contract is concluded, as the relationship between a man and a strange woman without marriage is not permissible.