It is certainly possible, but you will a need a modem for that. Your phone line will be used by the modem, though modems usually have an output slot to connect your phone to the modem, so that you still can use it in the traditional manner.
Obviously you will also need some software that understands the modem hardware, can sort out voice calls and faxes, and transferring incoming faxes to the PC.
The last time I used something like that was a decade ago and it was a commercial product restricted to Windows98. Modems are quite passť in these days of ADSL, but the technology is still available.
I suggest that you Google for modem hardware and sort out which ones support incoming faxes on Linux.