Sup guy's

Of course it is possible to marry your German girlfriend.
If you want to marry in Germany, there's a lot of buerocracy involved, you'll need to get several documents from your country (officially translated into German). The whole process will take several months and will cost you a lot. If you want to try that, your German girlfriend should approach the nearest Standesamt (family registry) and ask for requirements and procedure.
You may prefer to marry in your country, or in any location that makes marrying a foreigner easier - Denmark, Las Vegas and Singapore are options. To get the foreign marriage recognised in Germany, you need to have it legalized in that country's German embassy and then submit the certificate to the family registry here. To get a visa based on the foreign marriage, you need to apply at that country's German embassy.

It should be possible to marry, it's a basic right. Some of Beppi's suggestions don't seem to fit since someone in Germany as an asylum seeker is not in the situation to go home or to other countries to marry. I think the very minimum one would need is an official document from the Ghana consulate that you are not married. Then one will have to get an official German translation from a certified translator.

Hopefully you have never been married because otherwise it can lead to serious complications. I have a friend who has a German passport and had gotten married and divorced in Australia. But the German authorities refused to accept the documentation of divorce, claiming he had to have a specific document  from Australia that hadn't been issued anymore for a few decades. He fought about this for about 2 years before giving up and moving to Canada.

You'll anyway have to have contact to the Ghana consulate so you should ask them for further advice on what is required.

I think that one can also assume that the situation might be scrutinized rather closely to make sure it is not just a marriage of convenience.

I understand all what you said <beppi> thank you very much and always blessed