Yes is the answer! Im 22 and had been on medication for anxiety up until Christmas 2011. It was awful! I decided I didnt want to be on the medication anymore and started to go to cognitive behavioural therapy instead. A few months down the line with the help of CBT I took the notion that running may help with my anxiety. I also was determined to lose weight and get in shape, something that I always failed at. I can honestly say that running has been my saviour the past 12months, it has helped so much in that im no longer as anxious and on edge as I used to be and my confidence has very much improved. I also managed to lose 3 stone which was an added bonus. No longer on any form of antidepression medication and in general feel my entire outlook on things has changed and running has played a major part in that for me.
Good luck to you and I hope you find the running helpful for your anxiety