Please refer yourself to the FAQ of the official Asgardia Website :

2 : Registration on the Asgardia website makes you a part of the Asgardia community. Once we are recognized, we will post procedures for obtaining citizenship – they will be similar to citizenship procedures in other countries. Once you are a citizen, you will get a passport, like you would in any country.

We understand there might be many important reasons one may have to change their citizenship or to apply for political asylum. But for now, Asgardia isn't yet recognized as a country and therefore, cannot issue legal passports.

If you require urgent assistance, please contact your nation's departments of international relations, foreign embassies, or the immigration division of a foreign government.