You can use a cell phone to send a fax if it is a smartphone and you are using an online fax service.
You cannot use a regular cell phone to send a fax by attaching a fax machine (or computer with a fax modem or fax software) to a cell phone. There are GSM fax machines and GSM fax modems on the market, however.
The simplest option – online fax service
The simplest option to send a fax with a cell phone is an online fax service. This connects to a server via the internet to send and receive faxes. Faxes can also be transmitted with email.
Alternatives – GSM fax machines and GSM fax modems
There are GSM fax machines on the market. These fax machines will connect via the cellular network to send and receive faxes.
As well, there are GSM fax modems on the market. These fax modems will let a computer send and receive faxes over a cellular network.
Both of these options will need a separate cell phone account for the GSM fax machine or fax modem.