Yes! its absolutely possible. In fact I do the same thing at home. However, if you're considering connecting a high-end or even mid-end system to your computer you may want to consider upgrading your audio card. May I recommend the HT Omega Claro Plus+, HT Omega Claro Halo, or ASUS Xonar Essence STX. They're around 150-200 USD.
I think a 6ft 3.5 to RCA interconnect is around 10-15 USD.

You want to connect it to the green stereo output jack on the sound card, not the headphone jack in the front.

http://www.radioshack.com/product/index.jsp?productId=2103865

Quote:
You want to connect it to the green stereo output jack on the sound card, not the headphone jack in the front.

http://www.radioshack.com/product/index.jsp?productId=2103865

I agree