To connect the Icom transceiver to the PC serial port, you need to use a signal converter circuit. You can build the interface using one of these circuits, or purchase the original Icom (CT-17) or compatible ones.
There are many interfaces of all prices and types available for sale, just search online for "CI-V Icom interface for sale".
There are two types of interfaces: USB or Serial. They are equivalent; serial interfaces are less susceptible to radio frequency interference but require a PC with an RS232 serial port. On the other hand, USB interfaces can be used on all PCs.
For those who also want to use the transceiver with digital modes such as PSK31, JT65, etc., you should look for an interface that also has audio connections for radio <--> PC.
Finally, for those who want to try soldering, here are some simple serial interface diagrams.
Transistor Interface
Interface using the IC MAX232
Offering greater speed and reliability compared to the transistor interface:
From I2WQ: USB Interface using the FTDI FT232R module for Arduino
PTT Interface using the serial port RTS connector
Interface for using the BKTkeyerCW plug-in