Have a look at the BCM 2835 Datasheet
, page 175. It lists the characteristics of the ttyAMA0 UART on the Pi.
It can support CTS and RTS on Broadcom GPIO 16 & 17, physical pins 36 & 11.
You must change these pins to 'ALT3' mode to use them with the serial port.
DTR and DCD are not supported by the Pi's hardware, but often you can set up serial port handshaking with just CTS and RTS.
You do not say which model Pi you are using. On models before the Pi 3B, ttyAMA0 is the default serial UART. On the Pi 3B you will need to add "dtoverlay=pi3-disable-bt" to your '/boot/config.txt' file. For more details see the '/boot/overlays/README' file, about halfway down.
Caution, the Pi's GPIO pins work at 3.3 Volts, they are not 5V tolerant, you will need level converters to connect them to a TTL or RS232 serial port.
Another alternative may be to look for a USB-Serial port converter which has the handshaking pins you require.
Hope this helps a little,