The H-series (including the T44H) are not able to process data from the serial port. Their serial port are really slave-only communication port that accept predefined host link commands.
Enter the M-series PLC, and you are able to use any of the M-series PLC (T100MD888+, 1616+, 2424+ or T100MX3224R+ and T100MX4832) to process serial port data very easily and control any output based on the data received from the serial port. The M-series PLC was originally designed with such an application in mind!
Ladder logic is not strictly necessary because most of the serial communication command are handled using the powerful TBASIC commands. You do need to know a bit of ladder logic so that you know how to trigger the custom function that processes the TBASIC command.
All M-series PLC has two or 3 serial ports (RS232 or RS485) and you can connect to your card reader using either direct DB9 cable or null modem cable. It depends on your swipe card reader.
