Steam is Windows software so the proper answer is no. Cedega (which isn't free) is a fork of Wine that allows you to run compatible Windows games on linux, Steam and associated games included. The problem most users don't see coming is most Steam updates make it not work with Cedega. The developers who work on Cedega usually fix these problems the same day but to continue to get access to the new versions they release you need to stay subscribed to their service and that'll set you back $5/month.
if that sounds good to you, then here is a link