Can. 1191 §1. A vow, that is, a deliberate and free promise made to God about a possible and better good, must be fulfilled by reason of the virtue of religion.
§2. Unless they are prohibited by law, all who possess suitable use of reason are capable of making a vow.
Can. 1192 §1. A vow is public if a legitimate superior accepts it in the name of the Church; otherwise, it is private.
Anyone can make a private vow. But one needs to know what one is doing and what is involved in a vow. It needs to be well defined.
But one can not make a vow of being a member of a third order (secular order) on ones own…that is and be a member…
Most third orders do not have vows by the way…rather they have solemn promises which are not binding in conscience…