thank you very much for sharing your question with the Wefugees Community.
I assume, you live in a camp (Gemeinschaftsunterkunft). Yes, it is possible for you, if your Social Affairs Office (Sozialamt) agrees with it.
If you want to rent an appartment in the same city or region, in which youre Social Affairs Office (Sozialamt) is responsible for und you can pay for the rent by yourself, you can apply for it in your Sozialamt. First you can contact your Sozialamt and ask them how you should proceed with it.
Actually, the procedure is like this: You find an appartment but don't sign its contract. You write an application for renting this appartment to the Sozialamt and attach the conract of the appartment with this application and send it to the Sozialamt.
If you get the permission for it and you rent the appartment outside the camp, make sure that you are no longer registered in the camp; otherwise, your Sozialamt will also expect the rent from you for your place in the camp.
If you want to rent an apparment in another city/region, which is not under the authority of your Sozialamt, you can then apply for it in your Foreigners Office (Ausländerbehörde).
You can also take the advice of your Social Worker in your camp on all this. He/she can advise you on this and can also help you write the application to the Sozialamt/Ausländerbehörde.
I hope my answer was useful for you and I'll be very pleased if you contact me again with further questions. I'm a member of the MBEON-staff and I‘ll be glad to guide you over a longer period of time. Mbeon is an online consultancy for migrants via the mbeon-app, which you can install on your smartphone for free. Download it via App Store or Google Play Store. You'll find me In the mbeon-app under my name „München, Herr Noori“ and get confidential one-to-one advice in a safe virtual room where nobody can wiretap messages. Further information: www.mbeon.de.