Yes, it is possible if your vessel has an internet connection on board.
There are two possibilities:
You are using a PC and connect the serial output of the AIS transponder/receiver to the serial port of the PC (you can also use a serial-to-USB converter). On the PC, you install software which can forward the AIS data to FleetMon, e.g. "AIS Dispatcher". It requires that your PC is running non-stop.
You are using a serial-to-IP converter instead of a PC. So you link your AIS transponder/receiver with the serial cable to the converter and connect the converter to your internet connection with the network cable. It requires that the converter is configured for sending AIS data to FleetMon.com. This has the advantage that you don't need a PC and software.
If you are interested in the second option, please contact us. We can likely support you and send you a serial-to-IP converter.