"our member" is correct and usable in written English.
You can use it to refer to someone who belongs to a club, group, organization, etc., for example: "Our members are invited to the annual meeting."
And you agree to the rules of our Member Agreement.
Some of our member associations are really, really trying.
"We examine every one of our member firms every year.
The Jewish Center mourns the passing of our member, Murray Klein, husband of our member, Edith Klein.
Our member tribes are changing this narrative by taking back control of our future.
And you agree to the rules of our Member Agreement, found online at our website.
Congregation Or Zarua mourns the death of our member, Rabbi Efry Spectre.
Congregation Or Zarua mourns the death of our member, Frances Freedman.
"...Now we are all facing grave challenges confronted by our member states.
The Jewish Center mourns the passing of our member, Dr. Jack Pollack.
Without security of demand, our member countries will have difficulty ensuring supply through collective actions.
