In a brief statement on the official Epic Games forums, PR Manager Dana Crowley shared the company's position on the Stop Piracy Online Act. The short story is that they do not support it in its current form.
Epic also acknowledges that they are a member of the Entertainment Software Association, which strongly supports the house bill that will be taken up again by the House Judiciary community on January 23.
From the Epic forums:
Some people have asked how Epic feels about the Stop Online Piracy Act (SOPA). This post is meant to provide answers.
Epic Games supports efforts that would stop overseas websites profiting from pirating our games, but we have to do that in a way that's compatible with freedom of speech and due process of law.
Thus, we do not support the current version of SOPA.
We are members of the Entertainment Software Association (ESA), a trade organization that is working with legislators to refine the bill.
Senior PR Manager
Epic Games, Inc.
We admire the fact that Epic Games is the first ESA member to come out against the bill. Some might argue that being a member of the ESA makes it easy for the company to publicly denounce the bill while letting the ESA do all the heavy lifting and take all the heat, but companies have to start somewhere and exiting the ESA at the drop of a hat isn't in their best interest either. Hopefully Epic is having a dialogue with the leadership of the trade group and asking them to reconsider their hard line position.