Yes, just connect the main stereo output from your mixer to the line input of your soundcard using whatever adaptors are required, make sure the signals stay stereo. You will need to have some software to record the mixdown into.
There is also Adobe Audition which is both a stereo recording editing program and a multi-tracking program in one, for about 300 bucks.
There are also some free options available on the web, like Audacity, and the Kristal Audio engine, Kristal is a 16 track recorder that uses VST plugins so you could easily use some of the excellent free pluins from digitalfishphones for your "home" mastering.