Hi Matt,
Yes, you can. You'll need a serial null-modem cable, but be sure to get one that's specific for the Amiga, because the serial port on the Amiga is exactly the other way around, i.e. female instead of male or vice versa, I forgot which.
On the Linux side you'll need to install and configure a PPP daemon. You can start it like this:
/usr/sbin/pppd /dev/tty.KeySerial1 76800 noauth local passive proxyarp asyncmap 0 silent persist 192.168.100.43:192.168.100.44
In this example (from my iMac) you'll need to replace /dev/tty.KeySerial1 with the device name of the serial port of your PC.
Replace 76800 with the desired baud rate. Start with something slow like 9600 to get things running and then gradually replace this with higher baud rates until you reach the fastest working and error free speed. Unfortunately you probably won't be able to increase the baud rate much further than 9600 on an unaccelerated A500, but your mileage may vary.
Next replace the IP addresses with the desired IP addresses you'd like to use for the PPP interface on the A500 and the PPP interface on the PC. Also make sure your Linux PC can act as a router. Make sure the following line is present in your /etc/sysctl.conf:
net.ipv4.ip_forward=1
Now on your A500 install AmiTCP and a PPP device. I use AmiPPP which is easy to configure, because it has a GUI and good documentation, but there are alternatives available on Aminet.
Good luck!