Seriously. There can be no standalone software for that. There has to be a way for data to get from your computer to common telephone network and that way is called a modem.
I suppose there could be a service of some sort where you send someone a document via e-mail for example and they will fax it on. Or maybe some VOIP software with a fax feature. In any case this only means that the "modem" thing is not in your room and you pay for someone to use theirs somewhere else.