As a “casual conjunction,” *since* can certainly be used to mean “because,” and it often is. I think you’ll find this usage in any reliable dictionary. You just have to be careful that the meaning of the sentence is clear, and that the reader will not think you are referring to time.
In the narrative portions of my fiction, I would tend to use “since” only in the sense of time. In dialogue, which is more casual, I wouldn’t hesitate to use it in the sense of “because.”