You have to be careful of chasing two goals at the same time. This is a big mistake a lot of people make.
That being said, there is still a possibility, but do not expect miracles, and you will still not do as good while dieting as when bulking.
The main goal of weight lifting is to prevent muscle loss. So pick a routine for the sole purpose of that maintenance. During the diet I am starting in about 4 weeks, I am going on Waterbury's 10X3 for fat loss:
You could chose another. Anyway Poliquin says that one of the reasons people have trouble making their arms grow is that they have too often neglected the brachialis, and you can work on this by adding in a set of reverse curls at the beginning of your workouts.
Next I would add in Waterbury's 100 reps program:
This uses low weights on the days you do not workout to help you recover. Simply performing 100 reps of hammer DB curls and lying dumbbell extensions for your triceps, split throughout the day with real light weight. This helps your arms recover on the days you do not workout, and is supposed to cause more capillaries to grow, feeding more blood to those muscles.
With the arms being a minor muscle group, contrary to most weightlifters beliefs, you may be more successful building them up then anything else while dieting, but that is not guaranteed, of course. Anyway at the worst, it could prepare your arms to grow during your next bulking cycle.