What distro are you using?
Most any external CDROM drive should be able to work for you. If you want to be able to boot from the external CDROM drive to install linux, be sure to set the external drive to be the first boot device in the computer's BIOS.
To see if the external CDROM drive is detected in linux, put a CD in the drive and run lsusb in the terminal This will list all usb devices that the computer detects.
Write back if need more help.
And welcome to the LQ forums!