Absolutely, especially if you're putting your profits back into the business. Keep good records of every expense related to your site. On Schedule C, you list how much you made and subtract how much you spent (or vice versa). The kicker is that if you spend more than you make, the loss is subtracted off on your 1040. (Assuming things haven't changed within the last few years.) Do the research suggested, though, to find out what's considered a legitimate business expense and what isn't, and how to handle different types of expenses - there are some practices that the IRS uses as flags for audits. Again, keep records on everything.
If you're making money - or even if you're trying to make money, it's not a hobby. But that's a good thing. You can't deduct hobby expenses!