Hello @Kakai and welcome to our community!
In short: Yes it is possible for you to get married here in Germany. You need to get in contact with Standesamt (registry office) and hand in your and your fiancés documents they require. A passport issued by your home country is mandatory for this.
We had a few questions similar to yours here on the platform quite recently. Please check out the information provided over there (some of them might not be directly related to the situation you’re in, but it’s good to keep these things in mind):
Feel free to ask further questions if anything remained unclear after you read through the links above :)