You can try adjusting your chair differently - there are websites out there that show the most ergonomic ways to adjust your work chair so you are positioned comfortably.
If that doesn't work, you may want to try seeing a good chiropractor. My arms used to fall asleep all the time - pins and needles all the way down to my fingers! It was awful. Well, I had had a sports injury to my neck years ago, and it turns out that there was pressure on my nerves leading down into my arms. After some chiropractic adjustment, I started to feel a lot better. It's amazing how being a little out of alignment can cause all kinds of problems.
I'd start by mentioning this to the HR department where you work - lots of times, companies have an ergonomics consultant they can send to ensure your desk is the proper height for you, etc. Since you don't have this issue at home, I'm guessing it's something about your chair or your desk that is causing this issue.