Welcome to Wefugees and thank you for your question!
If you ask whether it's possible to get married to your same-sex partner in Germany, the answer is yes. Same-sex marriage has (finally) been legal in Germany since the first of October 2017.
On this Berlin Welcome Center website, you can find a more detailed explanation on marriage procedures in Germany: https://www.berlin.de/willkommenszentrum/en/families/marriage-and-civil-unions/
Here is a Wikipedia article that can be interesting, too: https://en.wikipedia.org/wiki/Same-sex_marriage_in_Germany
Also, regarding your status as an asylum-seeker: we have a Wefugees Blog Article on "How to Marry in Germany", please have a look! https://wefugees.wordpress.com/2018/04/20/heiraten-in-deutschland-how-to-marry/
I hope this answers your question. Feel free to get back to us if you need any further assistance :-)
All the best,