Does beer have antioxidants? We have both bad news and good news for you. The bad news is that lighter varieties, such as Bud Light whose value is reflected above, come in with extremely low numbers. In fact, at just 80, even a fast food hamburger comes in with a higher value of 110. Of course both are practically nothing when compared to almost every fruit and vegetable. For example, romaine lettuce (which is not particularly nutritious) comes in at over over 1,000. That means you're getting 10x more antioxidants from even a mediocre salad, assuming their weight is equal to the weight of the beer you're comparing it to (since the ORAC value is based per 100 grams of the food or beverage).
As you may know, many darker fruits and veggies - from acai to kale - often have more antioxidants. That begs the question, does dark beer contain more antioxidants? Well not more than wine, but the good news is that they often contain double (or more) than a light beer. Sorry, that's not an excuse to binge drink, because even a score of 200 or 300 is still incredibly low!
But, to help you rationalize your drinking, we bring you another glimmer of hope. We were able to dig up a study (albeit an old one - from nearly 20 years ago) that beer increases plasma antioxidant capacity in humans (source). In plain English, they're saying that beer may help with the expression or activation of antioxidant activity in your blood's plasma. This might be due to the metabolism of ethanol, rather than the antioxidants coming from the drink. Since this was only one study involving 14 participants, its hard to draw a conclusion one way or another over this.
Conclusion? Not to gang up on good ol' Bud Light, but if you want higher ORAC value (relatively, speaking) choose a dark, Indian pale ale, or a stout.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010