Yup, you can use a file instead of a partition

Boot to Linux
Log in as root
Go somewhere convienent - I put mine on the root directory - and create a file with all 0s in it

dd if=/dev/zero of=/swapfile bs=1024 count=500000

This creates a 500mb file.

Then make it a swapfile -

mkswap /swapfile

Then enable it
swapon /swapfile

Then you'll want an entry in /etc/fstab for it as well... same as a regular swap partition, but instead of a /dev/... device just put the path to the swapfile.