Hello and welcome to the Wefugees Community!
I assume you are holding a residence permit according to section 23 (4) of the German Residence Act and you moved to Germany within the so-called resettlement programme?
Unfortunately, I am not very familiar with the family reunification process for resettlement refugees and tried to make some research. In general, resettlement refugees can bring their families to Germany (as I read here and also here) and are also entitled for the privileged procedure - that means without being able to fully cover the costs of living (of the whole family) - IF they let the immigration office know about the planned family reunification within the first 3 months after the issuing of the first residence permit ("Fristwahrende Anzeige").
However, I am afraid that you may face diffciulties if your marriage is not officially recognized. As there are many contingencies, I would highly recommend you to get individual support in an experienced refugee/migration counselling office or by a lawyer.
Please let us know if you need help in finding such an organization close-by or if you have any other questions.
I will also link my colleague dear @mbeon-Christine here, maybe she can correct me if needed or add some information.
All the best,