It can take around a month in my experience with SSRIs like Celexa. Meds like these will affect people in different ways, however, I have had a positive experience with them. I think another thing you should be doing (if you are not already) is going through counseling to confront and learn about your anxiety. In my opinion, medications like Celexa are a great tool to use while you are going through therapy. While they will not 'cure' you of anything, they helped me tremendously.
I did notice I would have an increase in my anxiety whenever I would start, stop, or adjust dosage (under a doctor's supervision of course), but after I adjusted to it, it worked well. Keep us posted!
I take 60 mgs of Celexa per day. 40 mgs did the trick until I tapered off Klonopin. I now take a small dose of that as well. When my dosage got increased it took about three weeks to see a difference. In fact I had a little bit of an increase in my anxiety at first. I went from 20 mgs to 40 then ended up at 60mgs. Each time it took about three weeks for the higher dose to help. I am assuming your slow increase is due to side-effects, otherwise you could probably increase a little more on each increment. It's gonna take awhile but it's worth it. Stick with it.