I think that first cousins are not allowed to marry, by law, in some places. But this would probably not be true in many countries. The social consequences are what would rule your decision then.
As the others say, certainly be more concerned about social consequences than genetic ones. If your marriage would ostracize you from your whole social world, think hard about it because you need that world once you marry. The one instance in which I would be concerned about the genetic issues is if, for example, your mother and her sister had married two guys from the same small village. The gene pool would be reduced on both sides, then. In such a case, in your shoes I would definitely be concerned enough to talk to a geneticist and get some testing for various obvious issues or conditions.
I would think about your cultural norms. In the US, it is something that we just don't do (majority of us anyway) but it is more common in other countries. What's the norm in your country?
So, your first cousin, correct?
If you're asking about the risks of procreating with a cousin...to be honest, the risk for birth defects is not much higher than it is among two strangers. That's a common misperception....that two first cousins making a family are certainly going to have children with severe defects. Not true. It wouldn't hurt to talk to a genetic specialist, to put your mind at ease though.
The other issues with this is that in most places, it's very taboo. You may face a lot of stigma and social issues that you must be prepared for. I'm not sure where you live, but here in the US, marrying a first cousin is illegal in many states, and definitely quite taboo. You may want to check on the legalities as well.
My personal feeling is, there are so many people in the world, why choose a mate who is closely related? It will add the stigma/acceptance issue, not to mention can be very confusing for the children of such a union.
Good luck to you!